##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=1.4 ## ## Trouble about Pi/2 ## $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) $array_y2_init[1 + 1] = exact_soln_y2p(x_start) $array_y2_init[2 + 1] = exact_soln_y2pp(x_start) $array_y2_init[3 + 1] = exact_soln_y2ppp(x_start) $glob_look_poles=true $glob_max_iter=20 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y1 (x) return(1.0 + sin(x)) end def exact_soln_y2 (x) return(1.0 + sin(x)) end def exact_soln_y2p (x) return( cos(x)) end def exact_soln_y2pp (x) return( -sin(x)) end def exact_soln_y2ppp (x) return( -cos(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 1.2999999999999998 estimated_steps 1299999.9999999998 step_error 7.692307692307694e-17 est_needed_step_err 7.692307692307694e-17 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.475466125514874e-184 estimated_step_error 2.475466125514874e-184 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6612575021518578e-176 estimated_step_error 1.6612575021518578e-176 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.114851449339245e-168 estimated_step_error 1.114851449339245e-168 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.481646952857931e-161 estimated_step_error 7.481646952857931e-161 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.020855692025195e-153 estimated_step_error 5.020855692025195e-153 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.369449168190198e-145 estimated_step_error 3.369449168190198e-145 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2612124147513845e-137 estimated_step_error 2.2612124147513845e-137 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.517491888835743e-129 estimated_step_error 1.517491888835743e-129 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0183956259651798e-121 estimated_step_error 1.0183956259651798e-121 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.83466025790867e-114 estimated_step_error 6.83466025790867e-114 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.587096248204525e-106 estimated_step_error 4.587096248204525e-106 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.078929868524917e-98 estimated_step_error 3.078929868524917e-98 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0670155792488036e-90 estimated_step_error 2.0670155792488036e-90 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3881985285577422e-82 estimated_step_error 1.3881985285577422e-82 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.330106382801208e-75 estimated_step_error 9.330106382801208e-75 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.280203627412161e-67 estimated_step_error 6.280203627412161e-67 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.239904976716618e-59 estimated_step_error 4.239904976716618e-59 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.879345661003233e-51 estimated_step_error 2.879345661003233e-51 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y2[1] (analytic) 1.0998334166468282 y2[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.0998334166468282 y1[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.11 y2[1] (analytic) 1.1097783008371749 y2[1] (numeric) 1.1097783008371749 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1097783008371749 y1[1] (numeric) 1.1097783008371749 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.12 y2[1] (analytic) 1.1197122072889194 y2[1] (numeric) 1.1197122072889194 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1197122072889194 y1[1] (numeric) 1.1197122072889194 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.13 y2[1] (analytic) 1.129634142619695 y2[1] (numeric) 1.129634142619695 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.129634142619695 y1[1] (numeric) 1.129634142619695 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.14 y2[1] (analytic) 1.1395431146442365 y2[1] (numeric) 1.1395431146442365 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1395431146442365 y1[1] (numeric) 1.1395431146442365 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.15000000000000002 y2[1] (analytic) 1.1494381324735992 y2[1] (numeric) 1.1494381324735992 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1494381324735992 y1[1] (numeric) 1.1494381324735992 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.16000000000000003 y2[1] (analytic) 1.159318206614246 y2[1] (numeric) 1.159318206614246 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.159318206614246 y1[1] (numeric) 1.159318206614246 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.17000000000000004 y2[1] (analytic) 1.1691823490669961 y2[1] (numeric) 1.1691823490669961 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1691823490669961 y1[1] (numeric) 1.1691823490669961 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.18000000000000005 y2[1] (analytic) 1.1790295734258243 y2[1] (numeric) 1.1790295734258243 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1790295734258243 y1[1] (numeric) 1.1790295734258243 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.19000000000000006 y2[1] (analytic) 1.1888588949765007 y2[1] (numeric) 1.1888588949765007 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1888588949765007 y1[1] (numeric) 1.1888588949765007 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.20000000000000007 y2[1] (analytic) 1.1986693307950613 y2[1] (numeric) 1.1986693307950613 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1986693307950613 y1[1] (numeric) 1.1986693307950613 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.21000000000000008 y2[1] (analytic) 1.2084598998460996 y2[1] (numeric) 1.2084598998460996 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.2084598998460996 y1[1] (numeric) 1.2084598998460996 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.22000000000000008 y2[1] (analytic) 1.2182296230808694 y2[1] (numeric) 1.2182296230808694 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.2182296230808694 y1[1] (numeric) 1.2182296230808694 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2300000000000001 y2[1] (analytic) 1.2279775235351884 y2[1] (numeric) 1.2279775235351884 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.2279775235351884 y1[1] (numeric) 1.2279775235351884 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2400000000000001 y2[1] (analytic) 1.2377026264271347 y2[1] (numeric) 1.2377026264271347 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.2377026264271347 y1[1] (numeric) 1.2377026264271347 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y2[1] (analytic) 1.247403959254523 y2[1] (numeric) 1.247403959254523 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.247403959254523 y1[1] (numeric) 1.247403959254523 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y2[1] (analytic) 1.2570805518921553 y2[1] (numeric) 1.257080551892155 absolute error 2.220446049250313e-16 relative error 1.7663514449476623e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2570805518921553 y1[1] (numeric) 1.257080551892155 absolute error 2.220446049250313e-16 relative error 1.7663514449476623e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y2[1] (analytic) 1.2667314366888314 y2[1] (numeric) 1.2667314366888311 absolute error 2.220446049250313e-16 relative error 1.7528940902062405e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2667314366888314 y1[1] (numeric) 1.2667314366888311 absolute error 2.220446049250313e-16 relative error 1.7528940902062405e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y2[1] (analytic) 1.2763556485641139 y2[1] (numeric) 1.2763556485641137 absolute error 2.220446049250313e-16 relative error 1.7396765954287822e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2763556485641139 y1[1] (numeric) 1.2763556485641137 absolute error 2.220446049250313e-16 relative error 1.7396765954287822e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y2[1] (analytic) 1.2859522251048356 y2[1] (numeric) 1.2859522251048354 absolute error 2.220446049250313e-16 relative error 1.726694045005672e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2859522251048356 y1[1] (numeric) 1.2859522251048354 absolute error 2.220446049250313e-16 relative error 1.726694045005672e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y2[1] (analytic) 1.2955202066613398 y2[1] (numeric) 1.2955202066613394 absolute error 4.440892098500626e-16 relative error 3.427883313333386e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2955202066613398 y1[1] (numeric) 1.2955202066613394 absolute error 4.440892098500626e-16 relative error 3.427883313333386e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y2[1] (analytic) 1.3050586364434436 y2[1] (numeric) 1.3050586364434433 absolute error 2.220446049250313e-16 relative error 1.7014147772712272e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3050586364434436 y1[1] (numeric) 1.3050586364434433 absolute error 2.220446049250313e-16 relative error 1.7014147772712272e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y2[1] (analytic) 1.3145665606161179 y2[1] (numeric) 1.3145665606161177 absolute error 2.220446049250313e-16 relative error 1.6891088787543956e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3145665606161179 y1[1] (numeric) 1.3145665606161177 absolute error 2.220446049250313e-16 relative error 1.6891088787543956e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y2[1] (analytic) 1.3240430283948685 y2[1] (numeric) 1.3240430283948683 absolute error 2.220446049250313e-16 relative error 1.677019554222607e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3240430283948685 y1[1] (numeric) 1.3240430283948683 absolute error 2.220446049250313e-16 relative error 1.677019554222607e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y2[1] (analytic) 1.3334870921408146 y2[1] (numeric) 1.3334870921408144 absolute error 2.220446049250313e-16 relative error 1.6651425141922832e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3334870921408146 y1[1] (numeric) 1.3334870921408144 absolute error 2.220446049250313e-16 relative error 1.6651425141922832e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y2[1] (analytic) 1.3428978074554516 y2[1] (numeric) 1.3428978074554514 absolute error 2.220446049250313e-16 relative error 1.653473582965823e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3428978074554516 y1[1] (numeric) 1.3428978074554514 absolute error 2.220446049250313e-16 relative error 1.653473582965823e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y2[1] (analytic) 1.35227423327509 y2[1] (numeric) 1.35227423327509 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.35227423327509 y1[1] (numeric) 1.35227423327509 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y2[1] (analytic) 1.3616154319649623 y2[1] (numeric) 1.361615431964962 absolute error 2.220446049250313e-16 relative error 1.630743892235389e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3616154319649623 y1[1] (numeric) 1.361615431964962 absolute error 2.220446049250313e-16 relative error 1.630743892235389e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y2[1] (analytic) 1.3709204694129828 y2[1] (numeric) 1.3709204694129828 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.3709204694129828 y1[1] (numeric) 1.3709204694129828 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y2[1] (analytic) 1.3801884151231616 y2[1] (numeric) 1.3801884151231616 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.3801884151231616 y1[1] (numeric) 1.3801884151231616 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y2[1] (analytic) 1.3894183423086508 y2[1] (numeric) 1.3894183423086506 absolute error 2.220446049250313e-16 relative error 1.5981119448594803e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3894183423086508 y1[1] (numeric) 1.3894183423086506 absolute error 2.220446049250313e-16 relative error 1.5981119448594803e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y2[1] (analytic) 1.3986093279844232 y2[1] (numeric) 1.398609327984423 absolute error 2.220446049250313e-16 relative error 1.587609924245438e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3986093279844232 y1[1] (numeric) 1.398609327984423 absolute error 2.220446049250313e-16 relative error 1.587609924245438e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y2[1] (analytic) 1.4077604530595704 y2[1] (numeric) 1.4077604530595702 absolute error 2.220446049250313e-16 relative error 1.57728969046153e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4077604530595704 y1[1] (numeric) 1.4077604530595702 absolute error 2.220446049250313e-16 relative error 1.57728969046153e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y2[1] (analytic) 1.416870802429211 y2[1] (numeric) 1.4168708024292107 absolute error 2.220446049250313e-16 relative error 1.567147862348056e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.416870802429211 y1[1] (numeric) 1.4168708024292107 absolute error 2.220446049250313e-16 relative error 1.567147862348056e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y2[1] (analytic) 1.4259394650659998 y2[1] (numeric) 1.4259394650659996 absolute error 2.220446049250313e-16 relative error 1.5571811452371433e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4259394650659998 y1[1] (numeric) 1.4259394650659996 absolute error 2.220446049250313e-16 relative error 1.5571811452371433e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y2[1] (analytic) 1.4349655341112304 y2[1] (numeric) 1.4349655341112302 absolute error 2.220446049250313e-16 relative error 1.5473863284288448e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4349655341112304 y1[1] (numeric) 1.4349655341112302 absolute error 2.220446049250313e-16 relative error 1.5473863284288448e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y2[1] (analytic) 1.44394810696552 y2[1] (numeric) 1.4439481069655198 absolute error 2.220446049250313e-16 relative error 1.5377602827546315e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.44394810696552 y1[1] (numeric) 1.4439481069655198 absolute error 2.220446049250313e-16 relative error 1.5377602827546315e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y2[1] (analytic) 1.4528862853790685 y2[1] (numeric) 1.4528862853790683 absolute error 2.220446049250313e-16 relative error 1.5282999582248675e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4528862853790685 y1[1] (numeric) 1.4528862853790683 absolute error 2.220446049250313e-16 relative error 1.5282999582248675e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y2[1] (analytic) 1.461779175541483 y2[1] (numeric) 1.4617791755414828 absolute error 2.220446049250313e-16 relative error 1.5190023817570114e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.461779175541483 y1[1] (numeric) 1.4617791755414828 absolute error 2.220446049250313e-16 relative error 1.5190023817570114e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y2[1] (analytic) 1.4706258881711582 y2[1] (numeric) 1.470625888171158 absolute error 2.220446049250313e-16 relative error 1.5098646549814355e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4706258881711582 y1[1] (numeric) 1.470625888171158 absolute error 2.220446049250313e-16 relative error 1.5098646549814355e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y2[1] (analytic) 1.4794255386042032 y2[1] (numeric) 1.479425538604203 absolute error 2.220446049250313e-16 relative error 1.500883952121877e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4794255386042032 y1[1] (numeric) 1.479425538604203 absolute error 2.220446049250313e-16 relative error 1.500883952121877e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y2[1] (analytic) 1.4881772468829078 y2[1] (numeric) 1.4881772468829075 absolute error 2.220446049250313e-16 relative error 1.492057517947673e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4881772468829078 y1[1] (numeric) 1.4881772468829075 absolute error 2.220446049250313e-16 relative error 1.492057517947673e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y2[1] (analytic) 1.496880137843737 y2[1] (numeric) 1.4968801378437369 absolute error 2.220446049250313e-16 relative error 1.4833826657950556e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.496880137843737 y1[1] (numeric) 1.4968801378437369 absolute error 2.220446049250313e-16 relative error 1.4833826657950556e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y2[1] (analytic) 1.5055333412048473 y2[1] (numeric) 1.505533341204847 absolute error 2.220446049250313e-16 relative error 1.474856775654889e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5055333412048473 y1[1] (numeric) 1.505533341204847 absolute error 2.220446049250313e-16 relative error 1.474856775654889e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y2[1] (analytic) 1.5141359916531134 y2[1] (numeric) 1.5141359916531132 absolute error 2.220446049250313e-16 relative error 1.4664772923243572e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5141359916531134 y1[1] (numeric) 1.5141359916531132 absolute error 2.220446049250313e-16 relative error 1.4664772923243572e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y2[1] (analytic) 1.5226872289306594 y2[1] (numeric) 1.5226872289306592 absolute error 2.220446049250313e-16 relative error 1.4582417236202013e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5226872289306594 y1[1] (numeric) 1.5226872289306592 absolute error 2.220446049250313e-16 relative error 1.4582417236202013e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y2[1] (analytic) 1.5311861979208836 y2[1] (numeric) 1.5311861979208834 absolute error 2.220446049250313e-16 relative error 1.4501476386512227e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5311861979208836 y1[1] (numeric) 1.5311861979208834 absolute error 2.220446049250313e-16 relative error 1.4501476386512227e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y2[1] (analytic) 1.5396320487339694 y2[1] (numeric) 1.5396320487339692 absolute error 2.220446049250313e-16 relative error 1.4421926661478455e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5396320487339694 y1[1] (numeric) 1.5396320487339692 absolute error 2.220446049250313e-16 relative error 1.4421926661478455e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y2[1] (analytic) 1.548023936791874 y2[1] (numeric) 1.5480239367918736 absolute error 4.440892098500626e-16 relative error 2.8687489856932924e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.548023936791874 y1[1] (numeric) 1.5480239367918736 absolute error 4.440892098500626e-16 relative error 2.8687489856932924e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y2[1] (analytic) 1.556361022912784 y2[1] (numeric) 1.5563610229127838 absolute error 2.220446049250313e-16 relative error 1.4266908619278262e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.556361022912784 y1[1] (numeric) 1.5563610229127838 absolute error 2.220446049250313e-16 relative error 1.4266908619278262e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y2[1] (analytic) 1.5646424733950357 y2[1] (numeric) 1.5646424733950353 absolute error 4.440892098500626e-16 relative error 2.838279143007391e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5646424733950357 y1[1] (numeric) 1.5646424733950353 absolute error 4.440892098500626e-16 relative error 2.838279143007391e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y2[1] (analytic) 1.5728674601004817 y2[1] (numeric) 1.572867460100481 absolute error 6.661338147750939e-16 relative error 4.2351554194689636e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5728674601004817 y1[1] (numeric) 1.572867460100481 absolute error 6.661338147750939e-16 relative error 4.2351554194689636e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y2[1] (analytic) 1.5810351605373054 y2[1] (numeric) 1.581035160537305 absolute error 4.440892098500626e-16 relative error 2.8088509410451158e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5810351605373054 y1[1] (numeric) 1.581035160537305 absolute error 4.440892098500626e-16 relative error 2.8088509410451158e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y2[1] (analytic) 1.58914475794227 y2[1] (numeric) 1.5891447579422695 absolute error 4.440892098500626e-16 relative error 2.7945170358495143e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.58914475794227 y1[1] (numeric) 1.5891447579422695 absolute error 4.440892098500626e-16 relative error 2.7945170358495143e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.39495039709646 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y2[1] (analytic) 1.5971954413623926 y2[1] (numeric) 1.597195441362392 absolute error 4.440892098500626e-16 relative error 2.780431238091055e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5971954413623926 y1[1] (numeric) 1.597195441362392 absolute error 4.440892098500626e-16 relative error 2.780431238091055e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.657244977756381 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y2[1] (analytic) 1.6051864057360399 y2[1] (numeric) 1.6051864057360397 absolute error 2.220446049250313e-16 relative error 1.3832948256449711e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6051864057360399 y1[1] (numeric) 1.6051864057360397 absolute error 2.220446049250313e-16 relative error 1.3832948256449711e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.923474785272502 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y2[1] (analytic) 1.6131168519734342 y2[1] (numeric) 1.6131168519734338 absolute error 4.440892098500626e-16 relative error 2.7529884726377908e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6131168519734342 y1[1] (numeric) 1.6131168519734338 absolute error 4.440892098500626e-16 relative error 2.7529884726377908e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.19378351834228 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y2[1] (analytic) 1.6209859870365602 y2[1] (numeric) 1.6209859870365597 absolute error 4.440892098500626e-16 relative error 2.7396239905931187e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6209859870365602 y1[1] (numeric) 1.6209859870365597 absolute error 4.440892098500626e-16 relative error 2.7396239905931187e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.468320970380367 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y2[1] (analytic) 1.628793024018469 y2[1] (numeric) 1.6287930240184685 absolute error 4.440892098500626e-16 relative error 2.726492582553123e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.628793024018469 y1[1] (numeric) 1.6287930240184685 absolute error 4.440892098500626e-16 relative error 2.726492582553123e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.7472433774236 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y2[1] (analytic) 1.6365371822219683 y2[1] (numeric) 1.6365371822219679 absolute error 4.440892098500626e-16 relative error 2.713590712599095e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6365371822219683 y1[1] (numeric) 1.6365371822219679 absolute error 4.440892098500626e-16 relative error 2.713590712599095e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.030713789573415 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y2[1] (analytic) 1.6442176872376915 y2[1] (numeric) 1.644217687237691 absolute error 4.440892098500626e-16 relative error 2.7009149293129102e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6442176872376915 y1[1] (numeric) 1.644217687237691 absolute error 4.440892098500626e-16 relative error 2.7009149293129102e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.31890246787234 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y2[1] (analytic) 1.6518337710215372 y2[1] (numeric) 1.6518337710215367 absolute error 4.440892098500626e-16 relative error 2.6884618636621422e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6518337710215372 y1[1] (numeric) 1.6518337710215367 absolute error 4.440892098500626e-16 relative error 2.6884618636621422e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.611987308687993 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y2[1] (analytic) 1.6593846719714735 y2[1] (numeric) 1.659384671971473 absolute error 4.440892098500626e-16 relative error 2.6762282269514477e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6593846719714735 y1[1] (numeric) 1.659384671971473 absolute error 4.440892098500626e-16 relative error 2.6762282269514477e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.910154297872179 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y2[1] (analytic) 1.6668696350036982 y2[1] (numeric) 1.6668696350036978 absolute error 4.440892098500626e-16 relative error 2.664210808837953e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6668696350036982 y1[1] (numeric) 1.6668696350036978 absolute error 4.440892098500626e-16 relative error 2.664210808837953e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.21359799717885 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y2[1] (analytic) 1.6742879116281455 y2[1] (numeric) 1.674287911628145 absolute error 4.440892098500626e-16 relative error 2.6524064754084752e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6742879116281455 y1[1] (numeric) 1.674287911628145 absolute error 4.440892098500626e-16 relative error 2.6524064754084752e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.52252206566312 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y2[1] (analytic) 1.6816387600233345 y2[1] (numeric) 1.6816387600233342 absolute error 2.220446049250313e-16 relative error 1.3204060836582419e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6816387600233345 y1[1] (numeric) 1.6816387600233342 absolute error 2.220446049250313e-16 relative error 1.3204060836582419e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.837139819049225 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y2[1] (analytic) 1.6889214451105516 y2[1] (numeric) 1.6889214451105514 absolute error 2.220446049250313e-16 relative error 1.3147124489883954e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6889214451105516 y1[1] (numeric) 1.6889214451105514 absolute error 2.220446049250313e-16 relative error 1.3147124489883954e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.15767483034966 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y2[1] (analytic) 1.6961352386273572 y2[1] (numeric) 1.696135238627357 absolute error 2.220446049250313e-16 relative error 1.3091208759080252e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6961352386273572 y1[1] (numeric) 1.696135238627357 absolute error 2.220446049250313e-16 relative error 1.3091208759080252e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.484361575345318 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y2[1] (analytic) 1.7032794192004106 y2[1] (numeric) 1.7032794192004104 absolute error 2.220446049250313e-16 relative error 1.3036299412886006e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7032794192004106 y1[1] (numeric) 1.7032794192004104 absolute error 2.220446049250313e-16 relative error 1.3036299412886006e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.173680471310746 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y2[1] (analytic) 1.7103532724176083 y2[1] (numeric) 1.710353272417608 absolute error 2.220446049250313e-16 relative error 1.298238255838036e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7103532724176083 y1[1] (numeric) 1.710353272417608 absolute error 2.220446049250313e-16 relative error 1.298238255838036e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.853414755320891 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y2[1] (analytic) 1.7173560908995231 y2[1] (numeric) 1.717356090899523 absolute error 2.220446049250313e-16 relative error 1.2929444633042176e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7173560908995231 y1[1] (numeric) 1.717356090899523 absolute error 2.220446049250313e-16 relative error 1.2929444633042176e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.539433610407594 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y2[1] (analytic) 1.724287174370143 y2[1] (numeric) 1.7242871743701427 absolute error 2.220446049250313e-16 relative error 1.2877472397029281e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.724287174370143 y1[1] (numeric) 1.7242871743701427 absolute error 2.220446049250313e-16 relative error 1.2877472397029281e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.23149286306448 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y2[1] (analytic) 1.7311458297268962 y2[1] (numeric) 1.731145829726896 absolute error 2.220446049250313e-16 relative error 1.2826452925693777e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7311458297268962 y1[1] (numeric) 1.731145829726896 absolute error 2.220446049250313e-16 relative error 1.2826452925693777e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.929360016563427 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y2[1] (analytic) 1.737931371109963 y2[1] (numeric) 1.7379313711099629 absolute error 2.220446049250313e-16 relative error 1.2776373602325751e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.737931371109963 y1[1] (numeric) 1.7379313711099629 absolute error 2.220446049250313e-16 relative error 1.2776373602325751e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.632813543213912 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y2[1] (analytic) 1.7446431199708599 y2[1] (numeric) 1.7446431199708594 absolute error 4.440892098500626e-16 relative error 2.5454444222236127e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7446431199708599 y1[1] (numeric) 1.7446431199708594 absolute error 4.440892098500626e-16 relative error 2.5454444222236127e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.341642227056186 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y2[1] (analytic) 1.7512804051402933 y2[1] (numeric) 1.7512804051402928 absolute error 4.440892098500626e-16 relative error 2.5357972860690295e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7512804051402933 y1[1] (numeric) 1.7512804051402928 absolute error 4.440892098500626e-16 relative error 2.5357972860690295e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.055644552832188 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y2[1] (analytic) 1.7578425628952774 y2[1] (numeric) 1.7578425628952772 absolute error 2.220446049250313e-16 relative error 1.2631654825749006e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7578425628952774 y1[1] (numeric) 1.7578425628952772 absolute error 2.220446049250313e-16 relative error 1.2631654825749006e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.774628137463628 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y2[1] (analytic) 1.7643289370255055 y2[1] (numeric) 1.7643289370255053 absolute error 2.220446049250313e-16 relative error 1.258521584412586e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7643289370255055 y1[1] (numeric) 1.7643289370255053 absolute error 2.220446049250313e-16 relative error 1.258521584412586e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.498409200613242 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y2[1] (analytic) 1.7707388788989697 y2[1] (numeric) 1.7707388788989695 absolute error 2.220446049250313e-16 relative error 1.2539658307107185e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7707388788989697 y1[1] (numeric) 1.7707388788989695 absolute error 2.220446049250313e-16 relative error 1.2539658307107185e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.226812071217179 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y2[1] (analytic) 1.7770717475268243 y2[1] (numeric) 1.777071747526824 absolute error 2.220446049250313e-16 relative error 1.2494971305129008e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7770717475268243 y1[1] (numeric) 1.777071747526824 absolute error 2.220446049250313e-16 relative error 1.2494971305129008e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.95966872715511 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y2[1] (analytic) 1.7833269096274837 y2[1] (numeric) 1.7833269096274835 absolute error 2.220446049250313e-16 relative error 1.2451144191583686e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7833269096274837 y1[1] (numeric) 1.7833269096274835 absolute error 2.220446049250313e-16 relative error 1.2451144191583686e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.696818365477075 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y2[1] (analytic) 1.789503739689951 y2[1] (numeric) 1.7895037396899505 absolute error 4.440892098500626e-16 relative error 2.4816333154297037e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.789503739689951 y1[1] (numeric) 1.7895037396899505 absolute error 4.440892098500626e-16 relative error 2.4816333154297037e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.43810700083247 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y2[1] (analytic) 1.7956016200363665 y2[1] (numeric) 1.795601620036366 absolute error 4.440892098500626e-16 relative error 2.473205664857155e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7956016200363665 y1[1] (numeric) 1.795601620036366 absolute error 4.440892098500626e-16 relative error 2.473205664857155e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.183387089951301 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y2[1] (analytic) 1.8016199408837776 y2[1] (numeric) 1.8016199408837772 absolute error 4.440892098500626e-16 relative error 2.464943908381789e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8016199408837776 y1[1] (numeric) 1.8016199408837772 absolute error 4.440892098500626e-16 relative error 2.464943908381789e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 11.932517180212715 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y2[1] (analytic) 1.8075581004051147 y2[1] (numeric) 1.8075581004051142 absolute error 4.440892098500626e-16 relative error 2.4568461160420358e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8075581004051147 y1[1] (numeric) 1.8075581004051142 absolute error 4.440892098500626e-16 relative error 2.4568461160420358e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 11.685361580502594 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y2[1] (analytic) 1.8134155047893743 y2[1] (numeric) 1.8134155047893736 absolute error 6.661338147750939e-16 relative error 3.673365607693227e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8134155047893743 y1[1] (numeric) 1.8134155047893736 absolute error 6.661338147750939e-16 relative error 3.673365607693227e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y2[1] (analytic) 1.8191915683009987 y2[1] (numeric) 1.8191915683009983 absolute error 4.440892098500626e-16 relative error 2.4411349392126512e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8191915683009987 y1[1] (numeric) 1.8191915683009983 absolute error 4.440892098500626e-16 relative error 2.4411349392126512e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y2[1] (analytic) 1.8248857133384506 y2[1] (numeric) 1.82488571333845 absolute error 6.661338147750939e-16 relative error 3.650276890800285e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8248857133384506 y1[1] (numeric) 1.82488571333845 absolute error 6.661338147750939e-16 relative error 3.650276890800285e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y2[1] (analytic) 1.830497370491971 y2[1] (numeric) 1.8304973704919705 absolute error 4.440892098500626e-16 relative error 2.4260576224193518e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.830497370491971 y1[1] (numeric) 1.8304973704919705 absolute error 4.440892098500626e-16 relative error 2.4260576224193518e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y2[1] (analytic) 1.8360259786005209 y2[1] (numeric) 1.8360259786005206 absolute error 2.220446049250313e-16 relative error 1.209376160866095e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8360259786005209 y1[1] (numeric) 1.8360259786005206 absolute error 2.220446049250313e-16 relative error 1.209376160866095e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y2[1] (analytic) 1.8414709848078967 y2[1] (numeric) 1.8414709848078967 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.8414709848078967 y1[1] (numeric) 1.8414709848078967 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0100000000000007 y2[1] (analytic) 1.8468318446180154 y2[1] (numeric) 1.8468318446180154 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.8468318446180154 y1[1] (numeric) 1.8468318446180154 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0200000000000007 y2[1] (analytic) 1.8521080219493633 y2[1] (numeric) 1.852108021949363 absolute error 2.220446049250313e-16 relative error 1.198875023991997e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8521080219493633 y1[1] (numeric) 1.852108021949363 absolute error 2.220446049250313e-16 relative error 1.198875023991997e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0300000000000007 y2[1] (analytic) 1.8572989891886036 y2[1] (numeric) 1.8572989891886036 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.8572989891886036 y1[1] (numeric) 1.8572989891886036 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0400000000000007 y2[1] (analytic) 1.8624042272433388 y2[1] (numeric) 1.8624042272433385 absolute error 2.220446049250313e-16 relative error 1.19224710552603e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8624042272433388 y1[1] (numeric) 1.8624042272433385 absolute error 2.220446049250313e-16 relative error 1.19224710552603e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0500000000000007 y2[1] (analytic) 1.8674232255940173 y2[1] (numeric) 1.867423225594017 absolute error 2.220446049250313e-16 relative error 1.1890427508975643e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8674232255940173 y1[1] (numeric) 1.867423225594017 absolute error 2.220446049250313e-16 relative error 1.1890427508975643e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0600000000000007 y2[1] (analytic) 1.8723554823449866 y2[1] (numeric) 1.8723554823449864 absolute error 2.220446049250313e-16 relative error 1.1859105122865712e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8723554823449866 y1[1] (numeric) 1.8723554823449864 absolute error 2.220446049250313e-16 relative error 1.1859105122865712e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0700000000000007 y2[1] (analytic) 1.877200504274682 y2[1] (numeric) 1.8772005042746818 absolute error 2.220446049250313e-16 relative error 1.1828496978314287e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.877200504274682 y1[1] (numeric) 1.8772005042746818 absolute error 2.220446049250313e-16 relative error 1.1828496978314287e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0800000000000007 y2[1] (analytic) 1.8819578068849478 y2[1] (numeric) 1.8819578068849476 absolute error 2.220446049250313e-16 relative error 1.1798596340082871e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8819578068849478 y1[1] (numeric) 1.8819578068849476 absolute error 2.220446049250313e-16 relative error 1.1798596340082871e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0900000000000007 y2[1] (analytic) 1.8866269144494876 y2[1] (numeric) 1.8866269144494874 absolute error 2.220446049250313e-16 relative error 1.1769396653064461e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8866269144494876 y1[1] (numeric) 1.8866269144494874 absolute error 2.220446049250313e-16 relative error 1.1769396653064461e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1000000000000008 y2[1] (analytic) 1.8912073600614356 y2[1] (numeric) 1.8912073600614354 absolute error 2.220446049250313e-16 relative error 1.174089153913922e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8912073600614356 y1[1] (numeric) 1.8912073600614354 absolute error 2.220446049250313e-16 relative error 1.174089153913922e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1100000000000008 y2[1] (analytic) 1.895698685680048 y2[1] (numeric) 1.8956986856800477 absolute error 2.220446049250313e-16 relative error 1.1713074794129362e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.895698685680048 y1[1] (numeric) 1.8956986856800477 absolute error 2.220446049250313e-16 relative error 1.1713074794129362e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1200000000000008 y2[1] (analytic) 1.9001004421765053 y2[1] (numeric) 1.900100442176505 absolute error 2.220446049250313e-16 relative error 1.1685940384850719e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9001004421765053 y1[1] (numeric) 1.900100442176505 absolute error 2.220446049250313e-16 relative error 1.1685940384850719e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1300000000000008 y2[1] (analytic) 1.9044121893788262 y2[1] (numeric) 1.904412189378826 absolute error 2.220446049250313e-16 relative error 1.1659482446258494e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9044121893788262 y1[1] (numeric) 1.904412189378826 absolute error 2.220446049250313e-16 relative error 1.1659482446258494e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1400000000000008 y2[1] (analytic) 1.9086334961158835 y2[1] (numeric) 1.9086334961158833 absolute error 2.220446049250313e-16 relative error 1.1633695278684859e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9086334961158835 y1[1] (numeric) 1.9086334961158833 absolute error 2.220446049250313e-16 relative error 1.1633695278684859e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1500000000000008 y2[1] (analytic) 1.9127639402605214 y2[1] (numeric) 1.912763940260521 absolute error 4.440892098500626e-16 relative error 2.3217146690332157e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9127639402605214 y1[1] (numeric) 1.9127639402605212 absolute error 2.220446049250313e-16 relative error 1.1608573345166078e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1600000000000008 y2[1] (analytic) 1.9168031087717674 y2[1] (numeric) 1.9168031087717667 absolute error 6.661338147750939e-16 relative error 3.475233380657095e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9168031087717674 y1[1] (numeric) 1.916803108771767 absolute error 4.440892098500626e-16 relative error 2.3168222537713968e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1700000000000008 y2[1] (analytic) 1.920750597736136 y2[1] (numeric) 1.9207505977361354 absolute error 6.661338147750939e-16 relative error 3.468091149159201e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.920750597736136 y1[1] (numeric) 1.9207505977361357 absolute error 4.440892098500626e-16 relative error 2.3120607661061344e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1800000000000008 y2[1] (analytic) 1.9246060124080206 y2[1] (numeric) 1.9246060124080202 absolute error 4.440892098500626e-16 relative error 2.3074291932322755e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9246060124080206 y1[1] (numeric) 1.9246060124080204 absolute error 2.220446049250313e-16 relative error 1.1537145966161378e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1900000000000008 y2[1] (analytic) 1.9283689672491668 y2[1] (numeric) 1.9283689672491666 absolute error 2.220446049250313e-16 relative error 1.1514632764588596e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9283689672491668 y1[1] (numeric) 1.9283689672491668 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2000000000000008 y2[1] (analytic) 1.9320390859672267 y2[1] (numeric) 1.9320390859672263 absolute error 4.440892098500626e-16 relative error 2.2985518930521042e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9320390859672267 y1[1] (numeric) 1.9320390859672265 absolute error 2.220446049250313e-16 relative error 1.1492759465260521e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2100000000000009 y2[1] (analytic) 1.9356160015533863 y2[1] (numeric) 1.9356160015533859 absolute error 4.440892098500626e-16 relative error 2.2943042912110074e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9356160015533863 y1[1] (numeric) 1.935616001553386 absolute error 2.220446049250313e-16 relative error 1.1471521456055037e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2200000000000009 y2[1] (analytic) 1.9390993563190677 y2[1] (numeric) 1.9390993563190675 absolute error 2.220446049250313e-16 relative error 1.1450914271176476e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9390993563190677 y1[1] (numeric) 1.9390993563190677 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2300000000000009 y2[1] (analytic) 1.942488801931698 y2[1] (numeric) 1.9424888019316975 absolute error 4.440892098500626e-16 relative error 2.2861867178252993e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.942488801931698 y1[1] (numeric) 1.9424888019316977 absolute error 2.220446049250313e-16 relative error 1.1430933589126497e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2400000000000009 y2[1] (analytic) 1.9457839994495392 y2[1] (numeric) 1.945783999449539 absolute error 2.220446049250313e-16 relative error 1.1411575230747481e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9457839994495392 y1[1] (numeric) 1.9457839994495392 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2500000000000009 y2[1] (analytic) 1.9489846193555866 y2[1] (numeric) 1.9489846193555862 absolute error 4.440892098500626e-16 relative error 2.2785670314673725e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9489846193555866 y1[1] (numeric) 1.9489846193555864 absolute error 2.220446049250313e-16 relative error 1.1392835157336862e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.260000000000001 y2[1] (analytic) 1.952090341590516 y2[1] (numeric) 1.9520903415905158 absolute error 2.220446049250313e-16 relative error 1.1374709468830974e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.952090341590516 y1[1] (numeric) 1.952090341590516 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.270000000000001 y2[1] (analytic) 1.9551008555846925 y2[1] (numeric) 1.9551008555846923 absolute error 2.220446049250313e-16 relative error 1.1357194402056903e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9551008555846925 y1[1] (numeric) 1.9551008555846925 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.280000000000001 y2[1] (analytic) 1.9580158602892253 y2[1] (numeric) 1.958015860289225 absolute error 2.220446049250313e-16 relative error 1.13402863290511e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9580158602892253 y1[1] (numeric) 1.9580158602892253 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.290000000000001 y2[1] (analytic) 1.9608350642060728 y2[1] (numeric) 1.9608350642060728 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9608350642060728 y1[1] (numeric) 1.960835064206073 absolute error 2.220446049250313e-16 relative error 1.1323981755443336e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.300000000000001 y2[1] (analytic) 1.963558185417193 y2[1] (numeric) 1.963558185417193 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.963558185417193 y1[1] (numeric) 1.9635581854171933 absolute error 2.220446049250313e-16 relative error 1.130827731890481e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.310000000000001 y2[1] (analytic) 1.9661849516127343 y2[1] (numeric) 1.966184951612734 absolute error 2.220446049250313e-16 relative error 1.1293169787659217e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9661849516127343 y1[1] (numeric) 1.9661849516127343 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.320000000000001 y2[1] (analytic) 1.9687151001182654 y2[1] (numeric) 1.9687151001182652 absolute error 2.220446049250313e-16 relative error 1.1278656059055602e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9687151001182654 y1[1] (numeric) 1.9687151001182657 absolute error 2.220446049250313e-16 relative error 1.1278656059055602e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.330000000000001 y2[1] (analytic) 1.9711483779210448 y2[1] (numeric) 1.9711483779210446 absolute error 2.220446049250313e-16 relative error 1.1264733158201925e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9711483779210448 y1[1] (numeric) 1.971148377921045 absolute error 2.220446049250313e-16 relative error 1.1264733158201925e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.340000000000001 y2[1] (analytic) 1.9734845416953197 y2[1] (numeric) 1.9734845416953193 absolute error 4.440892098500626e-16 relative error 2.2502796473316597e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9734845416953197 y1[1] (numeric) 1.97348454169532 absolute error 2.220446049250313e-16 relative error 1.1251398236658299e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.350000000000001 y2[1] (analytic) 1.9757233578266593 y2[1] (numeric) 1.9757233578266589 absolute error 4.440892098500626e-16 relative error 2.247729714237781e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9757233578266593 y1[1] (numeric) 1.9757233578266598 absolute error 4.440892098500626e-16 relative error 2.247729714237781e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.360000000000001 y2[1] (analytic) 1.9778646024353164 y2[1] (numeric) 1.977864602435316 absolute error 4.440892098500626e-16 relative error 2.2452963125143245e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9778646024353164 y1[1] (numeric) 1.9778646024353168 absolute error 4.440892098500626e-16 relative error 2.2452963125143245e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.370000000000001 y2[1] (analytic) 1.9799080613986144 y2[1] (numeric) 1.979908061398614 absolute error 4.440892098500626e-16 relative error 2.2429789468928992e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9799080613986144 y1[1] (numeric) 1.9799080613986149 absolute error 4.440892098500626e-16 relative error 2.2429789468928992e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.380000000000001 y2[1] (analytic) 1.98185353037236 y2[1] (numeric) 1.9818535303723595 absolute error 4.440892098500626e-16 relative error 2.2407771464656374e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.98185353037236 y1[1] (numeric) 1.9818535303723603 absolute error 4.440892098500626e-16 relative error 2.2407771464656374e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.390000000000001 y2[1] (analytic) 1.9837008148112767 y2[1] (numeric) 1.9837008148112762 absolute error 4.440892098500626e-16 relative error 2.238690464480713e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9837008148112767 y1[1] (numeric) 1.9837008148112771 absolute error 4.440892098500626e-16 relative error 2.238690464480713e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 4 ) = y1 - 1.0; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations 130 Total Elapsed Time 4.0 Seconds Elapsed Time(since restart) 4.0 Seconds Time to Timeout 2 Minutes 56.0 Seconds Percent Done 100.76923076923084%