(%i1) batch("diffeq.max")
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load("stringproc")
(%i3) alias(convfloat,float)
(%i4) alias(int_trunc,truncate)
(%i5) alias(elapsed_time_seconds,elapsed_real_time)
(%i6) alias(ln,log)
(%i7) alias(arcsin,asin)
(%i8) alias(arccos,acos)
(%i9) alias(arctan,atan)
(%i10) alias(float_abs,abs)
(%i11) keepfloat:true
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_ats],
fixnum),convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_att],
fixnum),convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(factorial_2([nnn],fixnum),fixnum)
(%i43) mode_declare(factorial_1([nnn],fixnum),fixnum)
(%i44) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum)
(%i45) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i46) mode_declare(elaped_time_seconds(),convfloat)
(%i47) mode_declare(Si([x],convfloat),convfloat)
(%i48) mode_declare(Ci([x],convfloat),convfloat)
(%i49) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i50) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i51) mode_declare(main_prog(),fixnum)
(%i52) define_variable(MAX_TERMS,30,fixnum)
(%i53) define_variable(glob_iolevel,5,fixnum)
(%i54) define_variable(glob_yes_pole,4,fixnum)
(%i55) define_variable(glob_no_pole,3,fixnum)
(%i56) define_variable(glob_not_given,0,fixnum)
(%i57) define_variable(glob_no_sing_tests,4,fixnum)
(%i58) define_variable(glob_ratio_test,1,fixnum)
(%i59) define_variable(glob_three_term_test,2,fixnum)
(%i60) define_variable(glob_six_term_test,3,fixnum)
(%i61) define_variable(glob_log_10,log(10.0),convfloat)
(%i62) define_variable(ALWAYS,1,fixnum)
(%i63) define_variable(INFO,2,fixnum)
(%i64) define_variable(DEBUGL,3,fixnum)
(%i65) define_variable(DEBUGMASSIVE,4,fixnum)
(%i66) define_variable(MAX_UNCHANGED,10,fixnum)
(%i67) define_variable(glob_check_sign,1.0,convfloat)
(%i68) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i69) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i70) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i71) define_variable(glob_percent_done,0.0,convfloat)
(%i72) define_variable(glob_subiter_method,3,fixnum)
(%i73) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i74) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i75) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i76) define_variable(glob_html_log,true,boolean)
(%i77) define_variable(glob_good_digits,0,fixnum)
(%i78) define_variable(glob_max_opt_iter,10,fixnum)
(%i79) define_variable(glob_dump,false,boolean)
(%i80) define_variable(glob_djd_debug,true,boolean)
(%i81) define_variable(glob_display_flag,true,boolean)
(%i82) define_variable(glob_djd_debug2,true,boolean)
(%i83) define_variable(glob_h_reason,0,fixnum)
(%i84) define_variable(glob_sec_in_minute,60,fixnum)
(%i85) define_variable(glob_min_in_hour,60.0,convfloat)
(%i86) define_variable(glob_hours_in_day,24.0,convfloat)
(%i87) define_variable(glob_days_in_year,365,fixnum)
(%i88) define_variable(glob_sec_in_hour,3600,fixnum)
(%i89) define_variable(glob_sec_in_day,86400,fixnum)
(%i90) define_variable(glob_sec_in_year,31536000,fixnum)
(%i91) define_variable(glob_almost_1,0.999,convfloat)
(%i92) define_variable(glob_clock_sec,0.0,convfloat)
(%i93) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i94) define_variable(glob_not_yet_finished,true,boolean)
(%i95) define_variable(glob_initial_pass,true,boolean)
(%i96) define_variable(glob_not_yet_start_msg,true,boolean)
(%i97) define_variable(glob_reached_optimal_h,false,boolean)
(%i98) define_variable(glob_optimal_done,false,boolean)
(%i99) define_variable(glob_disp_incr,0.1,convfloat)
(%i100) define_variable(glob_h,0.1,convfloat)
(%i101) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i102) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i103) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i104) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i107) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i108) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i109) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i110) define_variable(glob_max_h,0.1,convfloat)
(%i111) define_variable(glob_min_h,1.0E-6,convfloat)
(%i112) define_variable(glob_type_given_pole,0,fixnum)
(%i113) define_variable(glob_large_float,1.0E+100,convfloat)
(%i114) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i115) define_variable(glob_least_given_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_ratio_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i118) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i119) define_variable(glob_last_good_h,0.1,convfloat)
(%i120) define_variable(glob_look_poles,false,boolean)
(%i121) define_variable(glob_display_interval,0.0,convfloat)
(%i122) define_variable(glob_next_display,0.0,convfloat)
(%i123) define_variable(glob_dump_analytic,false,boolean)
(%i124) define_variable(glob_abserr,1.0E-11,convfloat)
(%i125) define_variable(glob_relerr,1.0E-11,convfloat)
(%i126) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i127) define_variable(glob_max_hours,0.0,convfloat)
(%i128) define_variable(glob_max_iter,1000,fixnum)
(%i129) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i130) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i131) define_variable(glob_no_eqs,0,fixnum)
(%i132) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i133) define_variable(glob_optimal_start,0.0,convfloat)
(%i134) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i135) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i136) define_variable(glob_small_float,0.0,convfloat)
(%i137) define_variable(glob_smallish_float,0.0,convfloat)
(%i138) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i139) define_variable(glob_warned,false,boolean)
(%i140) define_variable(glob_warned2,false,boolean)
(%i141) define_variable(glob_max_sec,10000.0,convfloat)
(%i142) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i143) define_variable(glob_start,0,fixnum)
(%i144) define_variable(glob_curr_iter_when_opt,0,fixnum)
(%i145) define_variable(glob_current_iter,0,fixnum)
(%i146) define_variable(glob_iter,0,fixnum)
(%i147) define_variable(glob_normmax,0.0,convfloat)
(%i148) define_variable(glob_max_minutes,0.0,convfloat)
(%i149) array(array_y_init,MAX_TERMS)
(%i150) array(array_norms,MAX_TERMS)
(%i151) array(array_fact_1,MAX_TERMS)
(%i152) array(array_1st_rel_error,2)
(%i153) array(array_last_rel_error,2)
(%i154) array(array_type_pole,2)
(%i155) array(array_type_real_pole,2)
(%i156) array(array_type_complex_pole,2)
(%i157) array(array_y,MAX_TERMS)
(%i158) array(array_x,MAX_TERMS)
(%i159) array(array_tmp0,MAX_TERMS)
(%i160) array(array_tmp1,MAX_TERMS)
(%i161) array(array_tmp2,MAX_TERMS)
(%i162) array(array_tmp3,MAX_TERMS)
(%i163) array(array_tmp4,MAX_TERMS)
(%i164) array(array_tmp5,MAX_TERMS)
(%i165) array(array_tmp6,MAX_TERMS)
(%i166) array(array_tmp7,MAX_TERMS)
(%i167) array(array_tmp8,MAX_TERMS)
(%i168) array(array_tmp9,MAX_TERMS)
(%i169) array(array_tmp10,MAX_TERMS)
(%i170) array(array_tmp11,MAX_TERMS)
(%i171) array(array_tmp12,MAX_TERMS)
(%i172) array(array_tmp13,MAX_TERMS)
(%i173) array(array_tmp14,MAX_TERMS)
(%i174) array(array_m1,MAX_TERMS)
(%i175) array(array_y_higher,2,MAX_TERMS)
(%i176) array(array_y_higher_work,2,MAX_TERMS)
(%i177) array(array_y_higher_work2,2,MAX_TERMS)
(%i178) array(array_y_set_initial,2,MAX_TERMS)
(%i179) array(array_given_rad_poles,2,3)
(%i180) array(array_given_ord_poles,2,3)
(%i181) array(array_rad_test_poles,2,4)
(%i182) array(array_ord_test_poles,2,4)
(%i183) array(array_fact_2,MAX_TERMS,MAX_TERMS)
(%i184) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i185) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i186) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i187) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (if vallen = 4
then printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel)
else printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel))
(%i188) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i189) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i190) logitem_time(fd,secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],convfloat]),
secs:secs_in,printf(fd,"
~%"),
if secs >= 0
then (years_int
:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int
:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if truncate(years_int) > 0.1
then printf(fd,
"~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(fd,
"~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(fd,
"~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(fd,
"~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(fd,"~d Seconds~%",
sec_int))
else printf(fd," 0.0 Seconds~%"),
printf(fd," | ~%")),0)
(%i191) omniout_timestr(secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],
convfloat]),secs:secs_in,
if secs >= 0
then (
years_int:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if years_int > 0
then printf(true,
"= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(true,
"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(true,
"= ~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(true,
"= ~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(true,"= ~d Seconds~%",
sec_int))
else printf(true,"= 0.0 Seconds~%")),0)
(%i192) zero_ats_ar(arr_a):=(
block(modedcclare([iii],fixnum),iii:1,
while iii <= MAX_TERMS do
(arr_a[iii]:0.0,iii:1+iii)),0)
(%i193) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block(
mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats],
convfloat]),ret_ats:0.0,
if jjj_ats <= mmm_ats
then (ma_ats:1+mmm_ats,iii_ats:jjj_ats,
while iii_ats <= mmm_ats do
(lll_ats:ma_ats-iii_ats,
if lll_ats <= MAX_TERMS and iii_ats <= MAX_TERMS
then ret_ats
:arr_a[iii_ats]*arr_b[lll_ats]+ret_ats,
iii_ats:1+iii_ats)),ret_ats)
(%i194) att(mmm_att,arr_aa,arr_bb,jjj_att):=block(
mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att],
fixnum]),ret_att:0.0,
if jjj_att < mmm_att
then (ma_att:2+mmm_att,iii_att:jjj_att,
while iii_att < mmm_att and iii_att <= MAX_TERMS do
(lll_att:ma_att-iii_att,al_att:lll_att-1,
if lll_att <= MAX_TERMS and iii_att <= MAX_TERMS
then ret_att
:arr_aa[iii_att]*arr_bb[lll_att]*al_att
+ret_att,iii_att:1+iii_att),
ret_att:ret_att/mmm_att),ret_att)
(%i195) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i196) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i197) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i198) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
if rel_error # -1.0
then (if rel_error > +1.0E-34
then (
good_digits
:3-floor(log10(rel_error)),
printf(file,"~d",good_digits))
else (good_digits:16,
printf(file,"~d",
good_digits)))
else printf(file,"Unknown"),
printf(file," | ")),0)
(%i199) log_revs(file,revs):=printf(file,revs)
(%i200) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i201) logitem_h_reason(file):=(printf(file,""),
if glob_h_reason = 1 then printf(file,"Max H")
elseif glob_h_reason = 2
then printf(file,"Display_interval")
elseif glob_h_reason = 3
then printf(file,"Optimal")
elseif glob_h_reason = 4
then printf(file,"Pole Accuracy")
elseif glob_h_reason = 5
then printf(file,"Min H (Pole)")
elseif glob_h_reason = 6 then printf(file,"Pole")
else printf(file,"Impossible"),
printf(file," | "),0)
(%i202) logstart(file):=(printf(file,""),0)
(%i203) logend(file):=(printf(file,"
~%"),0)
(%i204) chk_data():=(
block(mode_declare([[errflag],boolean]),errflag:false,
if glob_max_iter < 2
then (omniout_str(ALWAYS,"Illegal max_iter"),
errflag:true),if errflag then quit()),0)
(%i205) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block(
mode_declare([[ms2,rrr,sec_left,sub1,sub2],
convfloat]),ms2:clock_sec2,
sub1:t_end2-t_start2,sub2:t2-t_start2,
if sub1 = 0.0 then sec_left:0.0
else (if sub2 > 0.0
then (rrr:sub1/sub2,
sec_left:rrr*ms2-ms2)
else sec_left:0.0),sec_left)
(%i206) comp_percent(t_end2,t_start2,t2):=block(
mode_declare([[rrr,sub1,sub2],convfloat]),
sub1:t_end2-t_start2,sub2:t2-t_start2,
if sub2 > glob_small_float then rrr:100.0*sub2/sub1
else rrr:0.0,rrr)
(%i207) comp_rad_from_ratio(term1,term2,last_no):=(
if term2 > 0.0 then ret:abs(term1*glob_h/term2)
else ret:glob_larger_float,ret)
(%i208) comp_ord_from_ratio(term1,term2,last_no):=(
if term2 > 0.0
then ret
:abs(term2)*convfloat(last_no)
*log(abs(term1*glob_h/term2))
/log(convfloat(last_no))
+1.0 else ret:glob_larger_float,ret)
(%i209) comp_rad_from_three_terms(term1,term2,term3,last_no):=(
temp:abs(
term1*term3
-term1*term3*convfloat(last_no)
-2.0*term2*term2
+term2*term2*convfloat(last_no)),
if temp > 0.0
then ret:abs(term2*glob_h*term1/temp)
else ret:glob_larger_float,ret)
(%i210) comp_ord_from_three_terms(term1,term2,term3,last_no):=(
ret:abs(
(-term1*term3*convfloat(last_no*last_no)
+term2*term2*convfloat(last_no*last_no)
+4.0*term2*term2
-4.0*term2*term2*convfloat(last_no)
-3.0*term1*term3
+4.0*term1*term3*convfloat(last_no))
/(term1*term3
-term1*term3*convfloat(last_no)
-2.0*term2*term2
+term2*term2*convfloat(last_no))),ret)
(%i211) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=
(
if term5 # 0.0 and term4 # 0.0 and term3 # 0.0
and term2 # 0.0 and term1 # 0.0
then (rm0:term6/term5,rm1:term5/term4,
rm2:term4/term3,rm3:term3/term2,
rm4:term2/term1,
nr1
:convfloat(last_no-3)*rm2
-2.0*convfloat(last_no-2)*rm1
+convfloat(last_no-1)*rm0,
nr2
:convfloat(last_no-4)*rm3
-2.0*convfloat(last_no-3)*rm2
+convfloat(last_no-2)*rm1,
dr1:(-1.0)/rm3+2.0/rm2+(-1.0)/rm1,
dr2:(-1.0)/rm4+2.0/rm3+(-1.0)/rm2,
ds1:5.0/rm3-8.0/rm2+3.0/rm1,
ds2:5.0/rm4-8.0/rm3+3.0/rm2,
if
abs(nr1*dr2-nr2*dr1) = 0.0
or abs(dr1) = 0.0
then (rad_c:glob_larger_float,
ord_no:glob_larger_float)
else (if
abs(nr1*dr2-nr2*dr1) # 0.0
then (
rcs
:(dr1*dr2-ds2*dr1+ds1*dr2)
/(nr1*dr2-nr2*dr1),
ord_no
:(rcs*nr1-ds1)/(2.0*dr1)
-convfloat(last_no)/2.0,
if abs(rcs) # 0.0
then (if rcs > 0.0
then rad_c
:sqrt(rcs)
*abs(glob_h)
else (
rad_c
:glob_larger_float,
ord_no
:glob_larger_float))
else (
rad_c:glob_larger_float,
ord_no:glob_larger_float))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float)))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float),
glob_six_term_ord_save:ord_no,rad_c)
(%i212) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i213) factorial_2(nnn):=nnn!
(%i214) factorial_1(nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= MAX_TERMS
then (if array_fact_1[nnn] = 0
then (ret:factorial_2(nnn),
array_fact_1[nnn]:ret)
else ret:array_fact_1[nnn])
else ret:factorial_2(nnn),ret)
(%i215) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= MAX_TERMS and mmm <= MAX_TERMS
then (if array_fact_2[mmm,nnn] = 0
then (ret:factorial_1(mmm)/factorial_1(nnn),
array_fact_2[mmm,nnn]:ret)
else ret:array_fact_2[mmm,nnn])
else ret:factorial_2(mmm)/factorial_2(nnn),ret)
(%i216) log10(x):=log(x)/glob_log_10
(%i217) expt(x,y):=(if x <= 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y),x^y)
(%i218) estimated_needed_step_error(x_start,x_end,estimated_h,
estimated_answer):=block(
[desired_abs_gbl_error,range,
estimated_steps,step_error],
omniout_float(ALWAYS,
"glob_desired_digits_correct",
32,
glob_desired_digits_correct,
32,""),
desired_abs_gbl_error
:expt(10.0,-glob_desired_digits_correct)
*abs(estimated_answer),
omniout_float(ALWAYS,"estimated_h",32,
estimated_h,32,""),
omniout_float(ALWAYS,"estimated_answer",
32,estimated_answer,32,""),
omniout_float(ALWAYS,
"desired_abs_gbl_error",32,
desired_abs_gbl_error,32,
""),range:x_end-x_start,
omniout_float(ALWAYS,"range",32,range,32,
""),
estimated_steps:range/estimated_h,
omniout_float(ALWAYS,"estimated_steps",32,
estimated_steps,32,""),
step_error
:abs(
desired_abs_gbl_error
/sqrt(estimated_steps)),
omniout_float(ALWAYS,"step_error",32,
step_error,32,""),
step_error)
(%i219) exact_soln_y(x):=block(1.0/(x-6.0)/(x-6.0)/(x-6.0)/(x-6.0)/(x-6.0))
1.0
-------
x - 6.0
-------
x - 6.0
-------
x - 6.0
-------
x - 6.0
(%o219) exact_soln_y(x) := block(-------)
x - 6.0
(%i220) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 1
or glob_type_given_pole = 2
then (rad_given
:sqrt(
array_given_rad_poles[1,2]
*array_given_rad_poles[1,2]
+(array_x[1]
-array_given_rad_poles[1,1])
*(array_x[1]
-array_given_rad_poles[1,1])),
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ",
4,rad_given,4," "),
omniout_float(ALWAYS,
"Order of pole (given) ",
4,
array_given_ord_poles[
1,1],4," "),
if rad_given < glob_least_given_sing
then glob_least_given_sing
:rad_given)
elseif glob_type_given_pole = 3
then omniout_str(ALWAYS,
"NO POLE (given) for Equation 1")
elseif glob_type_given_pole = 5
then omniout_str(ALWAYS,
"SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS,
"NO INFO (given) for Equation 1"),
if array_rad_test_poles[1,1] < glob_large_float
then (omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ",
4,
array_rad_test_poles[1,1],
4," "),
if
array_rad_test_poles[1,1]
< glob_least_ratio_sing
then glob_least_ratio_sing
:array_rad_test_poles[1,1],
omniout_float(ALWAYS,
"Order of pole (ratio test) ",
4,
array_ord_test_poles[1,1],
4," "))
else omniout_str(ALWAYS,
"NO POLE (ratio test) for Equation 1"),
if array_rad_test_poles[1,2] > 0.0
and array_rad_test_poles[1,2]
< glob_large_float
then (omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ",
4,
array_rad_test_poles[1,2],
4," "),
if
array_rad_test_poles[1,2]
< glob_least_3_sing
then glob_least_3_sing
:array_rad_test_poles[1,2],
omniout_float(ALWAYS,
"Order of pole (three term test) ",
4,
array_ord_test_poles[1,2],
4," "))
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1"),
if array_rad_test_poles[1,3] > 0.0
and array_rad_test_poles[1,3]
< glob_large_float
then (omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ",
4,
array_rad_test_poles[1,3],
4," "),
if
array_rad_test_poles[1,3]
< glob_least_6_sing
then glob_least_6_sing
:array_rad_test_poles[1,3],
omniout_float(ALWAYS,
"Order of pole (six term test) ",
4,
array_ord_test_poles[1,3],
4," "))
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")),
0)
(%i221) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0
else ret:-1.0,ret)
(%i222) est_size_answer():=block([min_size],
min_size:glob_estimated_size_answer,
if abs(array_y[1]) < min_size
then (min_size:abs(array_y[1]),
omniout_float(ALWAYS,"min_size",32,min_size,
32,"")),
if min_size < 1.0
then (min_size:1.0,
omniout_float(ALWAYS,"min_size",32,min_size,
32,"")),min_size)
(%i223) test_suggested_h():=block(
[max_estimated_step_error,hn_div_ho,hn_div_ho_2,
hn_div_ho_3,no_terms,est_tmp],
max_estimated_step_error:0.0,no_terms:MAX_TERMS,
hn_div_ho:0.5,hn_div_ho_2:0.25,hn_div_ho_3:0.125,
omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""),
omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,
""),
omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,
""),
est_tmp:abs(array_y[no_terms]*hn_div_ho_3
+array_y[no_terms-1]*hn_div_ho_2
+array_y[no_terms-2]*hn_div_ho
+array_y[no_terms-3]),
if est_tmp >= max_estimated_step_error
then max_estimated_step_error:est_tmp,
omniout_float(ALWAYS,"max_estimated_step_error",32,
max_estimated_step_error,32,""),
max_estimated_step_error)
(%i224) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display
then ret:true else ret:false,return(ret))
(%i225) display_alot(iter):=(
block(mode_declare(
[[abserr],convfloat,[analytic_val_y],convfloat,
[ind_var],convfloat,[numeric_val],convfloat,
[relerr],convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(ALWAYS,
"x[1] ",
33,ind_var,20,
" "),
analytic_val_y
:exact_soln_y(ind_var),
omniout_float(ALWAYS,
"y[1] (analytic) ",
33,
analytic_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val-analytic_val_y),
omniout_float(ALWAYS,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if abs(analytic_val_y) # 0.0
then (
relerr
:abserr*100.0
/abs(analytic_val_y),
if relerr > 1.0E-34
then glob_good_digits
:3-floor(log10(relerr))
else glob_good_digits
:16)
else (relerr:-1.0,
glob_good_digits:-1),
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
omniout_float(ALWAYS,
"absolute error ",
4,abserr,20," "),
omniout_float(ALWAYS,
"relative error ",
4,relerr,20,"%"),
omniout_int(INFO,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(ALWAYS,
"h ",
4,glob_h,20,
" ")))),0)
(%i226) prog_report(x_start,x_end):=(
block(mode_declare([[clock_sec],convfloat,[opt_clock_sec],
convfloat,[clock_sec1],convfloat,
[expect_sec],convfloat,[left_sec],
convfloat,[percent_done],convfloat,
[total_clock_sec],convfloat]),
clock_sec1:elapsed_time_seconds(),
total_clock_sec:clock_sec1-glob_orig_start_sec,
glob_clock_sec:clock_sec1-glob_clock_start_sec,
left_sec:-clock_sec1+glob_orig_start_sec
+glob_max_sec,
expect_sec:comp_expect_sec(x_end,x_start,
glob_h+array_x[1],
clock_sec1
-glob_orig_start_sec),
opt_clock_sec:clock_sec1
-glob_optimal_clock_start_sec,
glob_optimal_expect_sec
:comp_expect_sec(x_end,x_start,glob_h+array_x[1],
opt_clock_sec),
glob_total_exp_sec
:total_clock_sec+glob_optimal_expect_sec,
percent_done:comp_percent(x_end,x_start,
glob_h+array_x[1]),
glob_percent_done:percent_done,
omniout_str_noeol(INFO,
"Total Elapsed Time "),
omniout_timestr(total_clock_sec),
omniout_str_noeol(INFO,
"Elapsed Time(since restart) "),
omniout_timestr(glob_clock_sec),
if percent_done < 100.0
then (omniout_str_noeol(INFO,
"Expected Time Remaining "),
omniout_timestr(expect_sec),
omniout_str_noeol(INFO,
"Optimized Time Remaining "),
omniout_timestr(glob_optimal_expect_sec),
omniout_str_noeol(INFO,
"Expected Total Time "),
omniout_timestr(glob_total_exp_sec)),
omniout_str_noeol(INFO,
"Time to Timeout "),
omniout_timestr(left_sec),
omniout_float(INFO,
"Percent Done ",33,
percent_done,4,"%")),0)
(%i227) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-3 and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,2]:glob_larger_float,
array_ord_test_poles[1,2]:glob_larger_float,
found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-4 and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,3]:glob_larger_float,
array_ord_test_poles[1,3]:glob_larger_float,
found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-7 and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
omniout_str(ALWAYS,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(ALWAYS,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:1.0,
while term <= MAX_TERMS do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i228) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_m1[1]*array_const_5D0[1],
array_tmp2[1]:array_x[1]-array_const_6D0[1],
array_tmp3[1]:array_tmp1[1]/array_tmp2[1],
array_tmp4[1]:array_x[1]-array_const_6D0[1],
array_tmp5[1]:array_tmp3[1]/array_tmp4[1],
array_tmp6[1]:array_x[1]-array_const_6D0[1],
array_tmp7[1]:array_tmp5[1]/array_tmp6[1],
array_tmp8[1]:array_x[1]-array_const_6D0[1],
array_tmp9[1]:array_tmp7[1]/array_tmp8[1],
array_tmp10[1]:array_x[1]-array_const_6D0[1],
array_tmp11[1]:array_tmp9[1]/array_tmp10[1],
array_tmp12[1]:array_x[1]-array_const_6D0[1],
array_tmp13[1]:array_tmp11[1]/array_tmp12[1],
array_tmp14[1]:array_tmp13[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= MAX_TERMS
then (
temporary
:array_tmp14[1]*expt(glob_h,1)
*factorial_3(0,1),
if 2 <= MAX_TERMS
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:temporary*1.0/glob_h,
array_y_higher[2,1]:temporary,0)),kkk:2,
array_tmp1[2]:array_m1[2]*array_const_5D0[1],
array_tmp2[2]:array_x[2],
array_tmp3[2]:(array_tmp1[2]
-array_tmp3[1]*array_tmp2[2])
/array_tmp2[1],array_tmp4[2]:array_x[2],
array_tmp5[2]:(array_tmp3[2]
-array_tmp5[1]*array_tmp4[2])
/array_tmp4[1],array_tmp6[2]:array_x[2],
array_tmp7[2]:(array_tmp5[2]
-array_tmp7[1]*array_tmp6[2])
/array_tmp6[1],array_tmp8[2]:array_x[2],
array_tmp9[2]:(array_tmp7[2]
-array_tmp9[1]*array_tmp8[2])
/array_tmp8[1],array_tmp10[2]:array_x[2],
array_tmp11[2]:(array_tmp9[2]
-array_tmp11[1]*array_tmp10[2])
/array_tmp10[1],
array_tmp12[2]:array_x[2],
array_tmp13[2]:(array_tmp11[2]
-array_tmp13[1]*array_tmp12[2])
/array_tmp12[1],
array_tmp14[2]:array_tmp13[2],
if not array_y_set_initial[1,3]
then (if 2 <= MAX_TERMS
then (
temporary
:array_tmp14[2]*expt(glob_h,1)
*factorial_3(1,2),
if 3 <= MAX_TERMS
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:temporary*2.0/glob_h,
array_y_higher[2,2]:temporary,0)),kkk:3,
array_tmp1[3]:array_m1[3]*array_const_5D0[1],
array_tmp3[3]:(array_tmp1[3]
-array_tmp3[2]*array_tmp2[2])
/array_tmp2[1],
array_tmp5[3]:(array_tmp3[3]
-array_tmp5[2]*array_tmp4[2])
/array_tmp4[1],
array_tmp7[3]:(array_tmp5[3]
-array_tmp7[2]*array_tmp6[2])
/array_tmp6[1],
array_tmp9[3]:(array_tmp7[3]
-array_tmp9[2]*array_tmp8[2])
/array_tmp8[1],
array_tmp11[3]:(array_tmp9[3]
-array_tmp11[2]*array_tmp10[2])
/array_tmp10[1],
array_tmp13[3]:(array_tmp11[3]
-array_tmp13[2]*array_tmp12[2])
/array_tmp12[1],
array_tmp14[3]:array_tmp13[3],
if not array_y_set_initial[1,4]
then (if 3 <= MAX_TERMS
then (
temporary
:array_tmp14[3]*expt(glob_h,1)
*factorial_3(2,3),
if 4 <= MAX_TERMS
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:temporary*3.0/glob_h,
array_y_higher[2,3]:temporary,0)),kkk:4,
array_tmp1[4]:array_m1[4]*array_const_5D0[1],
array_tmp3[4]:(array_tmp1[4]
-array_tmp3[3]*array_tmp2[2])
/array_tmp2[1],
array_tmp5[4]:(array_tmp3[4]
-array_tmp5[3]*array_tmp4[2])
/array_tmp4[1],
array_tmp7[4]:(array_tmp5[4]
-array_tmp7[3]*array_tmp6[2])
/array_tmp6[1],
array_tmp9[4]:(array_tmp7[4]
-array_tmp9[3]*array_tmp8[2])
/array_tmp8[1],
array_tmp11[4]:(array_tmp9[4]
-array_tmp11[3]*array_tmp10[2])
/array_tmp10[1],
array_tmp13[4]:(array_tmp11[4]
-array_tmp13[3]*array_tmp12[2])
/array_tmp12[1],
array_tmp14[4]:array_tmp13[4],
if not array_y_set_initial[1,5]
then (if 4 <= MAX_TERMS
then (
temporary
:array_tmp14[4]*expt(glob_h,1)
*factorial_3(3,4),
if 5 <= MAX_TERMS
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:temporary*4.0/glob_h,
array_y_higher[2,4]:temporary,0)),kkk:5,
array_tmp1[5]:array_m1[5]*array_const_5D0[1],
array_tmp3[5]:(array_tmp1[5]
-array_tmp3[4]*array_tmp2[2])
/array_tmp2[1],
array_tmp5[5]:(array_tmp3[5]
-array_tmp5[4]*array_tmp4[2])
/array_tmp4[1],
array_tmp7[5]:(array_tmp5[5]
-array_tmp7[4]*array_tmp6[2])
/array_tmp6[1],
array_tmp9[5]:(array_tmp7[5]
-array_tmp9[4]*array_tmp8[2])
/array_tmp8[1],
array_tmp11[5]:(array_tmp9[5]
-array_tmp11[4]*array_tmp10[2])
/array_tmp10[1],
array_tmp13[5]:(array_tmp11[5]
-array_tmp13[4]*array_tmp12[2])
/array_tmp12[1],
array_tmp14[5]:array_tmp13[5],
if not array_y_set_initial[1,6]
then (if 5 <= MAX_TERMS
then (
temporary
:array_tmp14[5]*expt(glob_h,1)
*factorial_3(4,5),
if 6 <= MAX_TERMS
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:temporary*5.0/glob_h,
array_y_higher[2,5]:temporary,0)),kkk:6,
while kkk <= MAX_TERMS do
(array_tmp1[kkk]:array_m1[kkk]*array_const_5D0[1],
array_tmp3[kkk]
:(-ats(kkk,array_tmp2,array_tmp3,2))
/array_tmp2[1],
array_tmp5[kkk]
:(-ats(kkk,array_tmp4,array_tmp5,2))
/array_tmp4[1],
array_tmp7[kkk]
:(-ats(kkk,array_tmp6,array_tmp7,2))
/array_tmp6[1],
array_tmp9[kkk]
:(-ats(kkk,array_tmp8,array_tmp9,2))
/array_tmp8[1],
array_tmp11[kkk]
:(-ats(kkk,array_tmp10,array_tmp11,2))
/array_tmp10[1],
array_tmp13[kkk]
:(-ats(kkk,array_tmp12,array_tmp13,2))
/array_tmp12[1],
array_tmp14[kkk]:array_tmp13[kkk],order_d:1,
if order_d+kkk <= MAX_TERMS
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:array_tmp14[kkk]*expt(glob_h,order_d)
*factorial_3(kkk-1,
-1+order_d
+kkk),
array_y[order_d+kkk]:temporary,
array_y_higher[1,order_d+kkk]:temporary,
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= MAX_TERMS
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:temporary*adj2/glob_h
else temporary:temporary,
array_y_higher[adj3,term]
:temporary),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%i229) exact_soln_y(x):=block(1.0/(x-6.0)/(x-6.0)/(x-6.0)/(x-6.0)/(x-6.0))
1.0
-------
x - 6.0
-------
x - 6.0
-------
x - 6.0
-------
x - 6.0
(%o229) exact_soln_y(x) := block(-------)
x - 6.0
(%i230) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:64,max_terms:30,
glob_html_log:true,term:1,
while term <= MAX_TERMS do
(array_y_init[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_norms[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_fact_1[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_1st_rel_error[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:0.0,term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= MAX_TERMS do (array_y[term]:0.0,term:1+term),
term:1,
while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term),
term:1,
while term <= MAX_TERMS do
(array_tmp0[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp1[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp2[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp3[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp4[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp5[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp6[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp7[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp8[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp9[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp10[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp11[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp12[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp13[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp14[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do (array_m1[term]:0.0,term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher[ord,term]:0.0,term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher_work[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher_work2[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_set_initial[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= MAX_TERMS do
(term:1,
while term <= MAX_TERMS do
(array_fact_2[ord,term]:0.0,term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_m1),zero_ats_ar(array_tmp0),
zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2),
zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4),
zero_ats_ar(array_tmp5),zero_ats_ar(array_tmp6),
zero_ats_ar(array_tmp7),zero_ats_ar(array_tmp8),
zero_ats_ar(array_tmp9),zero_ats_ar(array_tmp10),
zero_ats_ar(array_tmp11),zero_ats_ar(array_tmp12),
zero_ats_ar(array_tmp13),zero_ats_ar(array_tmp14),
zero_ats_ar(array_const_1),array_const_1[1]:1,
zero_ats_ar(array_const_0D0),array_const_0D0[1]:0.0,
zero_ats_ar(array_const_5D0),array_const_5D0[1]:5.0,
zero_ats_ar(array_const_6D0),array_const_6D0[1]:6.0,
zero_ats_ar(array_m1),array_m1[1]:-1.0,iiif:0,
while iiif <= MAX_TERMS do
(jjjf:0,
while jjjf <= MAX_TERMS do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,ALWAYS:1,INFO:2,DEBUGL:3,
DEBUGMASSIVE:4,MAX_TERMS:30,glob_iolevel:INFO,
glob_orig_start_sec:elapsed_time_seconds(),
glob_curr_iter_when_opt:0,glob_display_flag:true,
glob_no_eqs:1,glob_iter:-1,opt_iter:-1,glob_max_iter:50000,
glob_max_hours:0.0,glob_max_minutes:15.0,
omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS,
"##############temp/sing7postode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "),
omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS,"Digits:64,"),
omniout_str(ALWAYS,"max_terms:30,"),omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS,"x_start:2.0,"),
omniout_str(ALWAYS,"x_end:3.0,"),
omniout_str(ALWAYS,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS,"glob_look_poles:true,"),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,""),
omniout_str(ALWAYS,"glob_type_given_pole:1,"),
omniout_str(ALWAYS,""),
omniout_str(ALWAYS,"array_given_rad_poles[1,1]:6.0,"),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,""),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"glob_desired_digits_correct:10,"),
omniout_str(ALWAYS,"glob_display_interval:0.01,"),
omniout_str(ALWAYS,"glob_look_poles:true,"),
omniout_str(ALWAYS,"glob_max_iter:100000000,"),
omniout_str(ALWAYS,"glob_max_minutes:10.0,"),
omniout_str(ALWAYS,"glob_subiter_method:3,"),
omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS,"exact_soln_y (x) := (block("),
omniout_str(ALWAYS,
" (1.0/ ( x - 6.0 ) / ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )) "),
omniout_str(ALWAYS,"));"),omniout_str(ALWAYS,""),
omniout_str(ALWAYS,""),
omniout_str(ALWAYS,"/* END USER DEF BLOCK */"),
omniout_str(ALWAYS,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:0.0,glob_smallish_float:0.0,
glob_large_float:1.0E+100,glob_larger_float:1.1E+100,
glob_almost_1:0.99,x_start:2.0,x_end:3.0,
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:1,
array_given_rad_poles[1,1]:6.0,
glob_desired_digits_correct:10,glob_display_interval:0.01,
glob_look_poles:true,glob_max_iter:100000000,
glob_max_minutes:10.0,glob_subiter_method:3,
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
omniout_str(ALWAYS,"START of Optimize"),
glob_check_sign:my_check_sign(x_start,x_end),found_h:false,
glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval:abs(glob_display_interval)
*glob_check_sign,chk_data(),
min_value:glob_larger_float,est_answer:est_size_answer(),
opt_iter:1,
est_needed_step_err:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(ALWAYS,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:0.0,
while opt_iter <= 100 and not found_h do
(omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""),
array_x[1]:x_start,array_x[2]:glob_h,
glob_next_display:x_start,order_diff:1,term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]*expt(glob_h,term_no-1)
/factorial_1(term_no-1),term_no:1+term_no),
rows:order_diff,r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < MAX_TERMS
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,term_no-1)
/factorial_1(term_no-1),
term_no:1+term_no),r_order:1+r_order),
atomall(),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(ALWAYS,"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (omniout_str(ALWAYS,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,found_h:true),
if glob_look_poles
then (check_for_pole(),
if opt_iter > 2 and not found_h
and (glob_min_pole_est
< 0.999*last_min_pole_est
or glob_min_pole_est
> 1.111
*last_min_pole_est)
then (
omniout_str(ALWAYS,
"SETTING H FOR POLE ACCURACY"),
glob_h_reason:4,found_h:true,
glob_h:glob_h/2.0,
last_min_pole_est:glob_min_pole_est)
else last_min_pole_est
:glob_min_pole_est),
if not found_h
then (est_answer:est_size_answer(),
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(ALWAYS,"est_needed_step_err",
32,est_needed_step_err,16,
""),
estimated_step_error:test_suggested_h(),
omniout_float(ALWAYS,
"estimated_step_error",32,
estimated_step_error,32,""),
if estimated_step_error
< est_needed_step_err
then (
omniout_str(ALWAYS,
"Double H and LOOP"),
glob_h:glob_h*2.0)
else (
omniout_str(ALWAYS,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/2.0)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(ALWAYS,"Beginning glob_h too large."),
found_h:false),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(ALWAYS,"START of Soultion"),
array_x[1]:x_start,array_x[2]:glob_h,
glob_next_display:x_start,
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,term_no-1)
/factorial_1(term_no-1),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < MAX_TERMS
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,term_no-1)
/factorial_1(term_no-1),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),
glob_current_iter:0,glob_iter:0,
omniout_str(DEBUGL," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_current_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(INFO," "),
omniout_str(INFO,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
glob_current_iter:1+glob_current_iter,
atomall(),display_alot(current_iter),
check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:2,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,calc_term-1)
/factorial_1(calc_term-1),ord:1,
calc_term:2,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:1,
calc_term:2,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,calc_term-1)
/factorial_1(calc_term-1),ord:1,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:1,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,calc_term-1)
/factorial_1(calc_term-1),
term_no:MAX_TERMS,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(ALWAYS,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(INFO,
"diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "),
omniout_int(INFO,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2014-01-20T02:41:09-06:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"sing7"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_good_digits(html_log_file,
array_last_rel_error[
1]),
logitem_integer(html_log_file,
MAX_TERMS),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if glob_percent_done < 100.0
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 249 | "),
logitem_str(html_log_file,
"sing7 diffeq.max"),
logitem_str(html_log_file,
"sing7 maxima results"),
logitem_str(html_log_file,
"All Tests - Maxima only - to save time"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i231) main():=(alias(convfloat,convfloat),compile(all),main_prog())
(%i232) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable fixnum in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable ALWAYS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable analytic_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable INFO in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable INFO in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_m1 in translation.
warning: encountered undefined variable array_const_5D0 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_6D0 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp5 in translation.
warning: encountered undefined variable array_tmp6 in translation.
warning: encountered undefined variable array_tmp7 in translation.
warning: encountered undefined variable array_tmp8 in translation.
warning: encountered undefined variable array_tmp9 in translation.
warning: encountered undefined variable array_tmp10 in translation.
warning: encountered undefined variable array_tmp11 in translation.
warning: encountered undefined variable array_tmp12 in translation.
warning: encountered undefined variable array_tmp13 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp14 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: encountered undefined variable INFO in translation.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ALWAYS in translation.
warning: variable x_start (declared type [found_h]) assigned type convfloat.
warning: variable x_end (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable x_start in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type [found_h].
warning: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable last_min_pole_est in translation.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable DEBUGL in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_current_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : |$debugmassive| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
Warning: modedcclare has a function or macro call which has not been translated properly.
The function was totaly undefined. Maybe you want to quote it."##############ECHO OF PROBLEM#################"
"##############temp/sing7postode.ode#################"
"diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:64,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:2.0,"
"x_end:3.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:1,"
""
"array_given_rad_poles[1,1]:6.0,"
""
""
""
""
""
""
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.01,"
"glob_look_poles:true,"
"glob_max_iter:100000000,"
"glob_max_minutes:10.0,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (1.0/ ( x - 6.0 ) / ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )) "
"));"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 1.000000E-6 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 1000000. ""
step_error = 1.0000000000000E-13 ""
est_needed_step_err = 1.0000000000000E-13 ""
opt_iter = 1
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 1.000000E-6 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 1000000. ""
step_error = 1.0000000000000E-13 ""
est_needed_step_err = 1.0000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 5.254211160650322000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-174 ""
estimated_step_error = 5.254211160650322000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-174 ""
"Double H and LOOP"
opt_iter = 2
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 2.000000E-6 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 500000. ""
step_error = 1.4142135623730950000000000000E-13 ""
est_needed_step_err = 1.4142135623730950000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.52604184650466060000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-166 ""
estimated_step_error = 3.52604184650466060000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-166 ""
"Double H and LOOP"
opt_iter = 3
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 4.000000E-6 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 250000. ""
step_error = 2.0000000000000E-13 ""
est_needed_step_err = 2.0000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.366287197015771700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-158 ""
estimated_step_error = 2.366287197015771700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-158 ""
"Double H and LOOP"
opt_iter = 4
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 8.000000E-6 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 125000. ""
step_error = 2.828427124746190000000000000E-13 ""
est_needed_step_err = 2.828427124746190000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.587989221482499000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-150 ""
estimated_step_error = 1.587989221482499000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-150 ""
"Double H and LOOP"
opt_iter = 5
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 1.600000E-5 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 62500. ""
step_error = 4.0000000000000E-13 ""
est_needed_step_err = 4.0000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.065682553193170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-142 ""
estimated_step_error = 1.065682553193170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-142 ""
"Double H and LOOP"
opt_iter = 6
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 3.200000E-5 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 31250. ""
step_error = 5.656854249492380000000000000E-13 ""
est_needed_step_err = 5.656854249492380000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 7.15168832658992000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-135 ""
estimated_step_error = 7.15168832658992000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-135 ""
"Double H and LOOP"
opt_iter = 7
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 6.400000E-5 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 15625. ""
step_error = 8.0000000000000E-13 ""
est_needed_step_err = 8.0000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.7994352795802770000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-127 ""
estimated_step_error = 4.7994352795802770000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-127 ""
"Double H and LOOP"
opt_iter = 8
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 1.280000E-4 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 7812.5 ""
step_error = 1.131370849898476000000000000E-12 ""
est_needed_step_err = 1.131370849898476000000000000E-12 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.22087130737170600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-119 ""
estimated_step_error = 3.22087130737170600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-119 ""
"Double H and LOOP"
opt_iter = 9
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 2.560000E-4 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 3906.25 ""
step_error = 1.6000000000000E-12 ""
est_needed_step_err = 1.6000000000000E-12 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.161523449266746200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-111 ""
estimated_step_error = 2.161523449266746200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-111 ""
"Double H and LOOP"
opt_iter = 10
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 5.120000E-4 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 1953.125 ""
step_error = 2.262741699796952000000000000E-12 ""
est_needed_step_err = 2.262741699796952000000000000E-12 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.45061853382117440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 ""
estimated_step_error = 1.45061853382117440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 ""
"Double H and LOOP"
opt_iter = 11
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 1.024000E-3 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 976.5625 ""
step_error = 3.2000000000000E-12 ""
est_needed_step_err = 3.2000000000000E-12 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 9.735536224832557000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-96 ""
estimated_step_error = 9.735536224832557000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-96 ""
"Double H and LOOP"
opt_iter = 12
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 2.048000E-3 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 488.28125 ""
step_error = 4.525483399593904000000000000E-12 ""
est_needed_step_err = 4.525483399593904000000000000E-12 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 6.5342132667754950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-88 ""
estimated_step_error = 6.5342132667754950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-88 ""
"Double H and LOOP"
opt_iter = 13
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 4.096000E-3 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 244.140625 ""
step_error = 6.4000000000000E-12 ""
est_needed_step_err = 6.4000000000000E-12 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.386117821653052000000000000000000000000000000000000000000000000000000000000000000000000000000000E-80 ""
estimated_step_error = 4.386117821653052000000000000000000000000000000000000000000000000000000000000000000000000000000000E-80 ""
"Double H and LOOP"
opt_iter = 14
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999964 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
min_size = 9.7656250000E-4 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 8.192000E-3 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1. ""
estimated_steps = 122.0703125 ""
step_error = 9.050966799187808000000000000E-12 ""
est_needed_step_err = 9.050966799187808000000000000E-12 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.944926520833646000000000000000000000000000000000000000000000000000000000000000000000000E-72 ""
estimated_step_error = 2.944926520833646000000000000000000000000000000000000000000000000000000000000000000000000E-72 ""
"Double H and LOOP"
opt_iter = 15
"SETTING H FOR DISPLAY INTERVAL"
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.4414062499999982 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2. " "
y[1] (analytic) = -9.7656250000E-4 " "
y[1] (numeric) = -9.7656250000E-4 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 4. " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9999999999999862 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.01 " "
y[1] (analytic) = -9.8886162072434670000E-4 " "
y[1] (numeric) = -9.8886162072432170000E-4 " "
absolute error = 2.493664996716660200000000000000000E-17 " "
relative error = 2.5217532407517610000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.99 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9899999999999807 " "
Order of pole (three term test) = 1.9790352399601110000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999999996 " "
y[1] (analytic) = -1.0013470890107976000E-3 " "
y[1] (numeric) = -1.001347089010747000E-3 " "
absolute error = 5.052382123782451000000000000000000E-17 " "
relative error = 5.045585271310427000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.9800000000000004 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9799999999999995 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999999994 " "
y[1] (analytic) = -1.0140222071652674000E-3 " "
y[1] (numeric) = -1.0140222071651908000E-3 " "
absolute error = 7.65446733774766100000000000000000E-17 " "
relative error = 7.548619037788115000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.9700000000000006 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.969999999999987 " "
Order of pole (three term test) = 7.46809359568548100000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.039999999999999 " "
y[1] (analytic) = -1.0268903445442867000E-3 " "
y[1] (numeric) = -1.0268903445441821000E-3 " "
absolute error = 1.04517089427602630000000000000000E-16 " "
relative error = 1.017801851803224600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.960000000000001 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9600000000000177 " "
Order of pole (three term test) = 1.29688593710732820000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.049999999999999 " "
y[1] (analytic) = -1.0399549390904728000E-3 " "
y[1] (numeric) = -1.0399549390903413000E-3 " "
absolute error = 1.31405303305243140000000000000000E-16 " "
relative error = 1.263567279368546800000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.950000000000001 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.95000000000001 " "
Order of pole (three term test) = 1.12566386298358970000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0599999999999987 " "
y[1] (analytic) = -1.0532194989071875000E-3 " "
y[1] (numeric) = -1.0532194989070268000E-3 " "
absolute error = 1.60678761962351760000000000000000E-16 " "
relative error = 1.525596156632789400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.9400000000000013 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.940000000000014 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0699999999999985 " "
y[1] (analytic) = -1.0666876038734437000E-3 " "
y[1] (numeric) = -1.066687603873254000E-3 " "
absolute error = 1.89735380184963280000000000000000E-16 " "
relative error = 1.77873427511466900000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.9300000000000015 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9299999999999877 " "
Order of pole (three term test) = 8.47138052422208600000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0799999999999983 " "
y[1] (analytic) = -1.0803629073002406000E-3 " "
y[1] (numeric) = -1.0803629073000201000E-3 " "
absolute error = 2.2052672188355160000000000000000E-16 " "
relative error = 2.04122818724528500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.9200000000000017 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9200000000000172 " "
Order of pole (three term test) = 1.46899770721117040000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999998 " "
y[1] (analytic) = -1.094249137629459100E-3 " "
y[1] (numeric) = -1.0942491376292082000E-3 " "
absolute error = 2.50884382713145700000000000000000E-16 " "
relative error = 2.29275376224332600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.910000000000002 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.910000000000018 " "
Order of pole (three term test) = 1.27320923187586480000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.099999999999998 " "
y[1] (analytic) = -1.1083501001765582000E-3 " "
y[1] (numeric) = -1.1083501001762748000E-3 " "
absolute error = 2.83410447887710860000000000000000E-16 " "
relative error = 2.557048064890002400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.900000000000002 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.9000000000000075 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999999977 " "
y[1] (analytic) = -1.122669678918285100E-3 " "
y[1] (numeric) = -1.1226696789179691000E-3 " "
absolute error = 3.159365130622760000000000000000E-16 " "
relative error = 2.814153788910440700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.8900000000000023 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.8900000000000374 " "
Order of pole (three term test) = 9.55386365394589400000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999999974 " "
y[1] (analytic) = -1.1372118383267135000E-3 " "
y[1] (numeric) = -1.1372118383263638000E-3 " "
absolute error = 3.49763620843823730000000000000000E-16 " "
relative error = 3.075624163027213500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.8800000000000026 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.8800000000000257 " "
Order of pole (three term test) = 1.65427609384210440000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999999972 " "
y[1] (analytic) = -1.1519806252509066000E-3 " "
y[1] (numeric) = -1.1519806252505214000E-3 " "
absolute error = 3.85108611666851200000000000000000E-16 " "
relative error = 3.34301292248706700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.8700000000000028 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.8699999999999872 " "
Order of pole (three term test) = 7.15839082644994900000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.139999999999997 " "
y[1] (analytic) = -1.1669801708475837000E-3 " "
y[1] (numeric) = -1.1669801708471625000E-3 " "
absolute error = 4.2110412379336990000000000000000E-16 " "
relative error = 3.60849425134207600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.860000000000003 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.859999999999986 " "
Order of pole (three term test) = 1.23856961653769780000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.149999999999997 " "
y[1] (analytic) = -1.1822146925621997000E-3 " "
y[1] (numeric) = -1.1822146925617412000E-3 " "
absolute error = 4.5840067852687130000000000000000E-16 " "
relative error = 3.877474044358093500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.850000000000003 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.8499999999999974 " "
Order of pole (three term test) = 1.07110541017189430000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1599999999999966 " "
y[1] (analytic) = -1.197688496161876100E-3 " "
y[1] (numeric) = -1.1976884961613794000E-3 " "
absolute error = 4.965645949983610300000000000000E-16 " "
relative error = 4.146024584770219000000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.8400000000000034 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.8400000000000105 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1699999999999964 " "
y[1] (analytic) = -1.2134059778216935000E-3 " "
y[1] (numeric) = -1.2134059778211585000E-3 " "
absolute error = 5.3494535190434790000000000000000E-16 " "
relative error = 4.408626310418231600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.8300000000000036 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.8299999999999863 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999996 " "
y[1] (analytic) = -1.229371626265886000E-3 " "
y[1] (numeric) = -1.2293716262653112000E-3 " "
absolute error = 5.7484399185181450000000000000000E-16 " "
relative error = 4.67591718866861400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.820000000000004 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.820000000000003 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.189999999999996 " "
y[1] (analytic) = -1.2455900249655255000E-3 " "
y[1] (numeric) = -1.2455900249649086000E-3 " "
absolute error = 6.169110361442520000000000000000E-16 " "
relative error = 4.95276153292353470000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.810000000000004 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.8100000000000076 " "
Order of pole (three term test) = 1.19360325362720330000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999999957 " "
y[1] (analytic) = -1.262065854394345000E-3 " "
y[1] (numeric) = -1.2620658543936852000E-3 " "
absolute error = 6.5962860174018090000000000000000E-16 " "
relative error = 5.22657830764886000000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.8000000000000043 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.800000000000027 " "
Order of pole (three term test) = 2.06050068072723770000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999999955 " "
y[1] (analytic) = -1.278803894344402000E-3 " "
y[1] (numeric) = -1.278803894343698800E-3 " "
absolute error = 7.0299668863960110000000000000000E-16 " "
relative error = 5.49729862216288300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.7900000000000045 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.78999999999998 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999999953 " "
y[1] (analytic) = -1.2958090263033237000E-3 " "
y[1] (numeric) = -1.2958090263025754000E-3 " "
absolute error = 7.4831633944949520000000000000000E-16 " "
relative error = 5.77489679620682600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.7800000000000047 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.7799999999999674 " "
Order of pole (three term test) = 1.53331767760829400000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.229999999999995 " "
y[1] (analytic) = -1.3130862358949397000E-3 " "
y[1] (numeric) = -1.313086235894145000E-3 " "
absolute error = 7.94720192431874800000000000000000E-16 " "
relative error = 6.05230769089761800000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.770000000000005 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.770000000000012 " "
Order of pole (three term test) = 1.32192544854879830000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.239999999999995 " "
y[1] (analytic) = -1.3306406153851785000E-3 " "
y[1] (numeric) = -1.3306406153843348000E-3 " "
absolute error = 8.43726130628219600000000000000000E-16 " "
relative error = 6.34075137097771100000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.760000000000005 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.7599999999999927 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2499999999999947 " "
y[1] (analytic) = -1.3484773662551341000E-3 " "
y[1] (numeric) = -1.348477366254242000E-3 " "
absolute error = 8.920815475210730000000000000000E-16 " "
relative error = 6.61547290184394400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.7500000000000053 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.749999999999992 " "
Order of pole (three term test) = 9.81391618381043600000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2599999999999945 " "
y[1] (analytic) = -1.3666018018433168000E-3 " "
y[1] (numeric) = -1.366601801842372800E-3 " "
absolute error = 9.4390641136588020000000000000000E-16 " "
relative error = 6.90696009688197900000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.7400000000000055 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.740000000000026 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2699999999999942 " "
y[1] (analytic) = -1.385019350059096000E-3 " "
y[1] (numeric) = -1.3850193500581007000E-3 " "
absolute error = 9.952975943416931000000000000000E-16 " "
relative error = 7.1861638200161290000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.7300000000000058 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.7299999999999907 " "
Order of pole (three term test) = 7.27421164960446700000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.279999999999994 " "
y[1] (analytic) = -1.4037355561695067000E-3 " "
y[1] (numeric) = -1.4037355561684564000E-3 " "
absolute error = 1.0501582242694596000000000000000E-15 " "
relative error = 7.48116851250185800000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.720000000000006 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.7200000000000126 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999994 " "
y[1] (analytic) = -1.4227560856615470000E-3 " "
y[1] (numeric) = -1.4227560856604426000E-3 " "
absolute error = 1.104585173328231900000000000000E-15 " "
relative error = 7.7637002186121500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.710000000000006 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.7099999999999973 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999999936 " "
y[1] (analytic) = -1.442086727182285100E-3 " "
y[1] (numeric) = -1.4420867271811233000E-3 " "
absolute error = 1.1618310480354666000000000000000E-15 " "
relative error = 8.05659622362370400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.7000000000000064 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.699999999999991 " "
Order of pole (three term test) = 1.8511767661570820000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999999934 " "
y[1] (analytic) = -1.4617333955590467000E-3 " "
y[1] (numeric) = -1.4617333955578250000E-3 " "
absolute error = 1.2218958483911635000000000000000E-15 " "
relative error = 8.3592250960637290000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.6900000000000066 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.689999999999995 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.319999999999993 " "
y[1] (analytic) = -1.4817021349021348000E-3 " "
y[1] (numeric) = -1.4817021349008527000E-3 " "
absolute error = 1.2819606487468604000000000000000E-15 " "
relative error = 8.65194574907954000000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.680000000000007 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.6799999999999855 " "
Order of pole (three term test) = 6.83280761985263700000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.329999999999993 " "
y[1] (analytic) = -1.5019991217925570000E-3 " "
y[1] (numeric) = -1.5019991217912124000E-3 " "
absolute error = 1.3446275343165226000000000000000E-15 " "
relative error = 8.95225246677761200000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.670000000000007 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.6700000000000212 " "
Order of pole (three term test) = 1.17341312395242760000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999999928 " "
y[1] (analytic) = -1.5226306685573116000E-3 " "
y[1] (numeric) = -1.5226306685559020000E-3 " "
absolute error = 1.4094628242311558000000000000000E-15 " "
relative error = 9.25676103428691700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.6600000000000072 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.659999999999998 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3499999999999925 " "
y[1] (analytic) = -1.543603226634907000E-3 " "
y[1] (numeric) = -1.5436032266334315000E-3 " "
absolute error = 1.4753823163182744000000000000000E-15 " "
relative error = 9.5580411524187100000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.6500000000000075 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.6500000000000283 " "
Order of pole (three term test) = 8.6407562209259900000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3599999999999923 " "
y[1] (analytic) = -1.5649233900338538000E-3 " "
y[1] (numeric) = -1.5649233900323095000E-3 " "
absolute error = 1.5441207340538554000000000000000E-15 " "
relative error = 9.86706917340184800000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.6400000000000077 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.640000000000005 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.369999999999992 " "
y[1] (analytic) = -1.5865978988869445000E-3 " "
y[1] (numeric) = -1.5865978988853300000E-3 " "
absolute error = 1.6145938752654132000000000000000E-15 " "
relative error = 1.01764528769268430000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.630000000000008 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.630000000000018 " "
Order of pole (three term test) = 1.27043468089842930000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999992 " "
y[1] (analytic) = -1.6086336431042747000E-3 " "
y[1] (numeric) = -1.6086336431025863000E-3 " "
absolute error = 1.6883196229944275000000000000000E-15 " "
relative error = 1.04953643748018240000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.620000000000008 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.6199999999999695 " "
Order of pole (three term test) = 2.17716470074936660000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3899999999999917 " "
y[1] (analytic) = -1.6310376661280016000E-3 " "
y[1] (numeric) = -1.6310376661262390000E-3 " "
absolute error = 1.762479051592436000000000000000E-15 " "
relative error = 1.08058758432996170000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.6100000000000083 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.6100000000000048 " "
Order of pole (three term test) = 9.32362173265952500000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3999999999999915 " "
y[1] (analytic) = -1.6538171687920006000E-3 " "
y[1] (numeric) = -1.6538171687901607000E-3 " "
absolute error = 1.839891086707901000000000000000E-15 " "
relative error = 1.11251178269712540000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.6000000000000085 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.600000000000011 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999999913 " "
y[1] (analytic) = -1.6769795132896115000E-3 " "
y[1] (numeric) = -1.6769795132876908000E-3 " "
absolute error = 1.9207725687753197000000000000000E-15 " "
relative error = 1.14537628727942930000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.5900000000000087 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.589999999999999 " "
Order of pole (three term test) = 1.3661565064724920000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.419999999999991 " "
y[1] (analytic) = -1.7005322272528467000E-3 " "
y[1] (numeric) = -1.700532227250844000E-3 " "
absolute error = 2.0025214125807267000000000000000E-15 " "
relative error = 1.17758509982238540000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.580000000000009 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.5799999999999845 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.429999999999991 " "
y[1] (analytic) = -1.7244830079465068000E-3 " "
y[1] (numeric) = -1.7244830079444196000E-3 " "
absolute error = 2.087089182034596000000000000000E-15 " "
relative error = 1.21026949666490270000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.570000000000009 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.5700000000000167 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999999906 " "
y[1] (analytic) = -1.74883972658076000E-3 " "
y[1] (numeric) = -1.7488397265785857000E-3 " "
absolute error = 2.1742590367024306000000000000000E-15 " "
relative error = 1.24325803197153360000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.5600000000000094 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.5600000000000107 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4499999999999904 " "
y[1] (analytic) = -1.7736104327458957000E-3 " "
y[1] (numeric) = -1.773610432743630800E-3 " "
absolute error = 2.2646814978877217000000000000000E-15 " "
relative error = 1.2768765091111650000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.5500000000000096 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.550000000000016 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.45999999999999 " "
y[1] (analytic) = -1.7988033589730557000E-3 " "
y[1] (numeric) = -1.7988033589706975000E-3 " "
absolute error = 2.358139725155972100000000000000E-15 " "
relative error = 1.31094914482606050000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.54000000000001 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.540000000000037 " "
Order of pole (three term test) = 1.24573023002248080000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.46999999999999 " "
y[1] (analytic) = -1.824426925424901000E-3 " "
y[1] (numeric) = -1.824426925422448000E-3 " "
absolute error = 2.4531158354657023000000000000000E-15 " "
relative error = 1.34459528155362130000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.53000000000001 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.5299999999999936 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4799999999999898 " "
y[1] (analytic) = -1.8504897447202992000E-3 " "
y[1] (numeric) = -1.8504897447177454000E-3 " "
absolute error = 2.553729797072357000000000000000E-15 " "
relative error = 1.38002915409744830000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.5200000000000102 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.5200000000000284 " "
Order of pole (three term test) = 9.07048448683247500000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4899999999999896 " "
y[1] (analytic) = -1.8770006268972297000E-3 " "
y[1] (numeric) = -1.8770006268945738000E-3 " "
absolute error = 2.6558616417204917000000000000000E-15 " "
relative error = 1.41494978939392030000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.5100000000000104 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.509999999999996 " "
Order of pole (three term test) = 7.73463550197141700000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999999893 " "
y[1] (analytic) = -1.9039685845183270000E-3 " "
y[1] (numeric) = -1.9039685845155657000E-3 " "
absolute error = 2.7614629333205800000000000000000E-15 " "
relative error = 1.450372110009990000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.5000000000000107 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.500000000000002 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.509999999999989 " "
y[1] (analytic) = -1.931402837923529000E-3 " "
y[1] (numeric) = -1.9314028379206596000E-3 " "
absolute error = 2.869232629265639000000000000000E-15 " "
relative error = 1.48556923130048840000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.490000000000011 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.4900000000000015 " "
Order of pole (three term test) = 1.1232986462589220000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.519999999999989 " "
y[1] (analytic) = -1.9593128206345464000E-3 " "
y[1] (numeric) = -1.959312820631564000E-3 " "
absolute error = 2.9824233360731256000000000000000E-15 " "
relative error = 1.52217823752474250000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.480000000000011 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.4799999999999898 " "
Order of pole (three term test) = 9.56552886973204100000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999999887 " "
y[1] (analytic) = -1.987708184915964000E-3 " "
y[1] (numeric) = -1.9877081849128658000E-3 " "
absolute error = 3.0982161280945775000000000000000E-15 " "
relative error = 1.5586876140098820000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.4700000000000113 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.4700000000000037 " "
Order of pole (three term test) = 1.62836556478406530000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999999885 " "
y[1] (analytic) = -2.0165988074980143000E-3 " "
y[1] (numeric) = -2.016598807494797000E-3 " "
absolute error = 3.217478367067983000000000000000E-15 " "
relative error = 1.5954975055548581000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.4600000000000115 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.460000000000021 " "
Order of pole (three term test) = 6.92680334781322500000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5499999999999883 " "
y[1] (analytic) = -2.045994795466177800E-3 " "
y[1] (numeric) = -2.045994795462836900E-3 " "
absolute error = 3.3410774147313305000000000000000E-15 " "
relative error = 1.63298431752367660000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.4500000000000117 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.450000000000027 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999988 " "
y[1] (analytic) = -2.075906492322994200E-3 " "
y[1] (numeric) = -2.0759064923195242000E-3 " "
absolute error = 3.4698806328226084000000000000000E-15 " "
relative error = 1.67150141186741040000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.440000000000012 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.4399999999999884 " "
Order of pole (three term test) = 1.00132280078266090000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999988 " "
y[1] (analytic) = -2.106344484227627200E-3 " "
y[1] (numeric) = -2.1063444842240264000E-3 " "
absolute error = 3.600852255258857300000000000000E-15 " "
relative error = 1.709526757005870000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.430000000000012 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.4300000000000166 " "
Order of pole (three term test) = 1.70138280579825360000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5799999999999876 " "
y[1] (analytic) = -2.137319606418954800E-3 " "
y[1] (numeric) = -2.1373196064152183000E-3 " "
absolute error = 3.7365943672540425000000000000000E-15 " "
relative error = 1.7482618678236180000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.4200000000000124 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.4199999999999915 " "
Order of pole (three term test) = 7.22375920011809400000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999999874 " "
y[1] (analytic) = -2.168842949828109200E-3 " "
y[1] (numeric) = -2.168842949824232000E-3 " "
absolute error = 3.877106968808164000000000000000E-15 " "
relative error = 1.787638412968279900000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.4100000000000126 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.409999999999996 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.599999999999987 " "
y[1] (analytic) = -2.2009258678866547000E-3 " "
y[1] (numeric) = -2.2009258678826316000E-3 " "
absolute error = 4.02325742165921000000000000000E-15 " "
relative error = 1.82798406814236370000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.400000000000013 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.4000000000000186 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.609999999999987 " "
y[1] (analytic) = -2.233579983536781700E-3 " "
y[1] (numeric) = -2.2335799835326084000E-3 " "
absolute error = 4.173311002331203700000000000000E-15 " "
relative error = 1.86844036617974050000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.390000000000013 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.3900000000000268 " "
Order of pole (three term test) = 8.82093082885417700000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.619999999999987 " "
y[1] (analytic) = -2.2668171964501350000E-3 " "
y[1] (numeric) = -2.2668171964458067000E-3 " "
absolute error = 4.328135072562133700000000000000E-15 " "
relative error = 1.90934455559100660000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.380000000000013 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.380000000000011 " "
Order of pole (three term test) = 7.47595248831648700000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999999866 " "
y[1] (analytic) = -2.300649690462113000E-3 " "
y[1] (numeric) = -2.3006496904576257000E-3 " "
absolute error = 4.487295951483006000000000000000E-15 " "
relative error = 1.95044728890545640000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.3700000000000134 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.3700000000000117 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999999864 " "
y[1] (analytic) = -2.3350899412287562000E-3 " "
y[1] (numeric) = -2.3350899412241033000E-3 " "
absolute error = 4.652962043438791000000000000000E-15 " "
relative error = 1.9926264771584510000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.3600000000000136 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.3600000000000025 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.649999999999986 " "
y[1] (analytic) = -2.370150724113549200E-3 " "
y[1] (numeric) = -2.3701507241087252000E-3 " "
absolute error = 4.823832305822506300000000000000E-15 " "
relative error = 2.03524284626525140000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.350000000000014 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.350000000000008 " "
Order of pole (three term test) = 1.81509977312701850000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999986 " "
y[1] (analytic) = -2.4058451223117847000E-3 " "
y[1] (numeric) = -2.4058451223067834000E-3 " "
absolute error = 5.001207781241135000000000000000E-15 " "
relative error = 2.0787737892435310000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.340000000000014 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.340000000000017 " "
Order of pole (three term test) = 1.5353007069053650000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6699999999999857 " "
y[1] (analytic) = -2.4421865352203545000E-3 " "
y[1] (numeric) = -2.442186535215171200E-3 " "
absolute error = 5.1833537462187000000000000000000E-15 " "
relative error = 2.12242335770269690000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.3300000000000143 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.3300000000000125 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6799999999999855 " "
y[1] (analytic) = -2.4791886870611776000E-3 " "
y[1] (numeric) = -2.4791886870558058000E-3 " "
absolute error = 5.372004924231177000000000000000E-15 " "
relative error = 2.1668398828485840000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.3200000000000145 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.3200000000000136 " "
Order of pole (three term test) = 1.09679129745240510000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999999853 " "
y[1] (analytic) = -2.516865635766714000E-3 " "
y[1] (numeric) = -2.5168656357611480000E-3 " "
absolute error = 5.5658602726715860000000000000000E-15 " "
relative error = 2.21142527180480770000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.3100000000000147 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.3100000000000214 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.699999999999985 " "
y[1] (analytic) = -2.555231782136383000E-3 " "
y[1] (numeric) = -2.555231782130615000E-3 " "
absolute error = 5.7679555576228840000000000000000E-15 " "
relative error = 2.25731207554110830000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.300000000000015 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.3000000000000083 " "
Order of pole (three term test) = 7.81937320245144200000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.709999999999985 " "
y[1] (analytic) = -2.5943018792729694000E-3 " "
y[1] (numeric) = -2.594301879266992500E-3 " "
absolute error = 5.976556055609095000000000000000E-15 " "
relative error = 2.3037242131914010000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.290000000000015 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.29000000000002 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999999847 " "
y[1] (analytic) = -2.634091042308497000E-3 " "
y[1] (numeric) = -2.6340910423023056000E-3 " "
absolute error = 6.1912280857612250000000000000000E-15 " "
relative error = 2.3504229680441420000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.2800000000000153 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.2800000000000082 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999999844 " "
y[1] (analytic) = -2.6746147584293417000E-3 " "
y[1] (numeric) = -2.6746147584229263000E-3 " "
absolute error = 6.415007414162233000000000000000E-15 " "
relative error = 2.3984790310247980000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.2700000000000156 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.2700000000000204 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999999842 " "
y[1] (analytic) = -2.7158888972107414000E-3 " "
y[1] (numeric) = -2.7158888972040970000E-3 " "
absolute error = 6.6448582747291600000000000000000E-15 " "
relative error = 2.4466605690510862000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.2600000000000158 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.260000000000005 " "
Order of pole (three term test) = 7.89963286423728500000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.749999999999984 " "
y[1] (analytic) = -2.7579297212712720000E-3 " "
y[1] (numeric) = -2.757929721264389000E-3 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 2.49585139881775660000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.250000000000016 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.2500000000000093 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999984 " "
y[1] (analytic) = -2.800753897258174700E-3 " "
y[1] (numeric) = -2.8007538972510426000E-3 " "
absolute error = 7.132315571478642000000000000000E-15 " "
relative error = 2.5465698997905140000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.240000000000016 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.240000000000044 " "
Order of pole (three term test) = 2.23873076268213840000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7699999999999836 " "
y[1] (analytic) = -2.844378507174893000E-3 " "
y[1] (numeric) = -2.844378507167508000E-3 " "
absolute error = 7.385151518102262000000000000000E-15 " "
relative error = 2.59640251797478850000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.2300000000000164 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.2300000000000204 " "
Order of pole (three term test) = 9.41439791019074700000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7799999999999834 " "
y[1] (analytic) = -2.8888210600626150000E-3 " "
y[1] (numeric) = -2.8888210600549640000E-3 " "
absolute error = 7.650997890795708000000000000000E-15 " "
relative error = 2.64848453113598950000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.2200000000000166 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.2200000000000224 " "
Order of pole (three term test) = 7.91370969653500200000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.789999999999983 " "
y[1] (analytic) = -2.9340995040479410000E-3 " "
y[1] (numeric) = -2.9340995040400186000E-3 " "
absolute error = 7.922915795655072000000000000000E-15 " "
relative error = 2.7002887205169634000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.210000000000017 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.210000000000031 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.799999999999983 " "
y[1] (analytic) = -2.980232238769452000E-3 " "
y[1] (numeric) = -2.980232238761246000E-3 " "
absolute error = 8.205675722239292000000000000000E-15 " "
relative error = 2.75336788035936530000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.200000000000017 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.2000000000000015 " "
Order of pole (three term test) = 1.11655489882301050000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999999827 " "
y[1] (analytic) = -3.0272381281962235000E-3 " "
y[1] (numeric) = -3.027238128187725000E-3 " "
absolute error = 8.498410308810378000000000000000E-15 " "
relative error = 2.80731476974166700000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.1900000000000173 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.1900000000000195 " "
Order of pole (three term test) = 9.37043055948971400000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999999825 " "
y[1] (analytic) = -3.075136513852002000E-3 " "
y[1] (numeric) = -3.0751365138432013000E-3 " "
absolute error = 8.800685874499337000000000000000E-15 " "
relative error = 2.86188461385584200000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.1800000000000175 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.1799999999999873 " "
Order of pole (three term test) = 7.85959222862795800000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999999823 " "
y[1] (analytic) = -3.123947228459174000E-3 " "
y[1] (numeric) = -3.1239472284500586000E-3 " "
absolute error = 9.115538185389127000000000000000E-15 " "
relative error = 2.9179552401994920000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.1700000000000177 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.1700000000000115 " "
Order of pole (three term test) = 1.31774074684002730000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.839999999999982 " "
y[1] (analytic) = -3.1736906100172270000E-3 " "
y[1] (numeric) = -3.1736906100077883000E-3 " "
absolute error = 9.438196751920813000000000000000E-15 " "
relative error = 2.9738868439572264000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.160000000000018 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.1600000000000197 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999982 " "
y[1] (analytic) = -3.2243875163310126000E-3 " "
y[1] (numeric) = -3.2243875163212393000E-3 " "
absolute error = 9.773432063653331000000000000000E-15 " "
relative error = 3.03109722828054760000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.150000000000018 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.1500000000000163 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8599999999999817 " "
y[1] (analytic) = -3.2760593400046184000E-3 " "
y[1] (numeric) = -3.2760593399944954000E-3 " "
absolute error = 1.012341252493165200000000000000E-14 " "
relative error = 3.0901187903749566000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.1400000000000183 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.1400000000000206 " "
Order of pole (three term test) = 7.7369819414828510000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8699999999999815 " "
y[1] (analytic) = -3.328728023917339000E-3 " "
y[1] (numeric) = -3.3287280239068556000E-3 " "
absolute error = 1.04833676461968400000000000000E-14 " "
relative error = 3.14936142901207140000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.1300000000000185 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.130000000000012 " "
Order of pole (three term test) = 1.29426792764883340000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8799999999999812 " "
y[1] (analytic) = -3.3824160771988776000E-3 " "
y[1] (numeric) = -3.38241607718802000E-3 " "
absolute error = 1.085763423613883600000000000000E-14 " "
relative error = 3.21002324620290440000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.1200000000000188 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.1199999999999912 " "
Order of pole (three term test) = 2.1638569537863840000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.889999999999981 " "
y[1] (analytic) = -3.4371465917214960000E-3 " "
y[1] (numeric) = -3.4371465917102520000E-3 " "
absolute error = 1.12440438904126700000000000000E-14 " "
relative error = 3.2713309107893140000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.110000000000019 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.110000000000015 " "
Order of pole (three term test) = 9.03905590129690100000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.899999999999981 " "
y[1] (analytic) = -3.492943259127624000E-3 " "
y[1] (numeric) = -3.492943259115981000E-3 " "
absolute error = 1.164303028988733500000000000000E-14 " "
relative error = 3.3333007226676870000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.100000000000019 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.100000000000008 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999999806 " "
y[1] (analytic) = -3.549830388412087000E-3 " "
y[1] (numeric) = -3.549830388400027000E-3 " "
absolute error = 1.206023128585975700000000000000E-14 " "
relative error = 3.3974105707215350000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.0900000000000194 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.09000000000001 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999999804 " "
y[1] (analytic) = -3.607832924078878000E-3 " "
y[1] (numeric) = -3.607832924066388000E-3 " "
absolute error = 1.249000902703301100000000000000E-14 " "
relative error = 3.4619144760484870000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.0800000000000196 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.080000000000004 " "
Order of pole (three term test) = 1.05053712952721120000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.92999999999998 " "
y[1] (analytic) = -3.6669764648932446000E-3 " "
y[1] (numeric) = -3.666976464880308000E-3 " "
absolute error = 1.293670032209704000000000000000E-14 " "
relative error = 3.5278929237615547000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.07000000000002 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.070000000000034 " "
Order of pole (three term test) = 8.75629347975569500000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.93999999999998 " "
y[1] (analytic) = -3.727287283250559000E-3 " "
y[1] (numeric) = -3.7272872832371634000E-3 " "
absolute error = 1.339553468149290400000000000000E-14 " "
relative error = 3.5939099037761020000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.06000000000002 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.0600000000000103 " "
Order of pole (three term test) = 7.29409080154892900000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9499999999999797 " "
y[1] (analytic) = -3.7887923451844396000E-3 " "
y[1] (numeric) = -3.7887923451705646000E-3 " "
absolute error = 1.387518572260049200000000000000E-14 " "
relative error = 3.66216579281149370000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.0500000000000203 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.0500000000000314 " "
Order of pole (three term test) = 1.21448535309297140000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9599999999999795 " "
y[1] (analytic) = -3.851519331037322000E-3 " "
y[1] (numeric) = -3.851519331022948000E-3 " "
absolute error = 1.437391872194382400000000000000E-14 " "
relative error = 3.73201261281805000000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.0400000000000205 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.0400000000000227 " "
Order of pole (three term test) = 0.0 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9699999999999793 " "
y[1] (analytic) = -3.915496656817760700E-3 " "
y[1] (numeric) = -3.915496656802875400E-3 " "
absolute error = 1.488566214735698200000000000000E-14 " "
relative error = 3.8017302661816077000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.0300000000000207 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.0300000000000327 " "
Order of pole (three term test) = 8.4021121515970200000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999979 " "
y[1] (analytic) = -3.98075349626962950E-3 " "
y[1] (numeric) = -3.980753496254209000E-3 " "
absolute error = 1.542082433969582700000000000000E-14 " "
relative error = 3.8738455807792930000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.020000000000021 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.020000000000019 " "
Order of pole (three term test) = 6.98216461408108600000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.989999999999979 " "
y[1] (analytic) = -4.047319803679339000E-3 " "
y[1] (numeric) = -4.047319803663363000E-3 " "
absolute error = 1.597593585200840500000000000000E-14 " "
relative error = 3.9472877427390330000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.010000000000021 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.0100000000000082 " "
Order of pole (three term test) = 1.15972502063308140000000000000E-13 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999999787 " "
y[1] (analytic) = -4.115226337448415000E-3 " "
y[1] (numeric) = -4.115226337431863000E-3 " "
absolute error = 1.655186404603270500000000000000E-14 " "
relative error = 4.02210296318608830000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
Radius of convergence (given) for eq 1 = 3.0000000000000213 " "
Order of pole (given) = 0.0 " "
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.0000000000000164 " "
Order of pole (three term test) = 9.62546098568050500000000000000E-14 " "
"NO COMPLEX POLE (six term test) for Equation 1"
"Finished!"
"diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "
Iterations = 101
"Total Elapsed Time "= 14 Seconds
"Elapsed Time(since restart) "= 13 Seconds
"Time to Timeout "= 9 Minutes 45 Seconds
Percent Done = 101.99999999999783 "%"
(%o232) diffeq.max