##############ECHO OF PROBLEM################# ##############temp/sing1postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-2.0 x_end=-1.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=500 $glob_max_h=0.5 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=4 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.001 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=1.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(1.0 / (x * x + 0.000001)) 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 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.5 estimated_steps 500000.0 step_error 2.0e-16 est_needed_step_err 2.0e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.484894657593405e-101 estimated_step_error 6.484894657593405e-101 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 4.249941687783492e-96 estimated_step_error 4.249941687783492e-96 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 2.785243259044777e-91 estimated_step_error 2.785243259044777e-91 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 1.825338954958387e-86 estimated_step_error 1.825338954958387e-86 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 1.1962566707722527e-81 estimated_step_error 1.1962566707722527e-81 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 7.839820921607223e-77 estimated_step_error 7.839820921607223e-77 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 5.137948560927475e-72 estimated_step_error 5.137948560927475e-72 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 3.3672630151535505e-67 estimated_step_error 3.3672630151535505e-67 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 2.2068442650790195e-62 estimated_step_error 2.2068442650790195e-62 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 1.4463754771965563e-57 estimated_step_error 1.4463754771965563e-57 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 9.480251350755155e-53 estimated_step_error 9.480251350755155e-53 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 6.214662514172606e-48 estimated_step_error 6.214662514172606e-48 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 4.075051566311024e-43 estimated_step_error 4.075051566311024e-43 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 2.673527639981127e-38 estimated_step_error 2.673527639981127e-38 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 1.7559389673284363e-33 estimated_step_error 1.7559389673284363e-33 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 1.1558064421947916e-28 estimated_step_error 1.1558064421947916e-28 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 7.64154872314529e-24 estimated_step_error 7.64154872314529e-24 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 5.097942655829754e-19 estimated_step_error 5.097942655829754e-19 best_h 0.262144 opt_iter 19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.465429033624368e-14 estimated_step_error 3.465429033624368e-14 best_h 0.131072 START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (analytic) 0.24999993750001562 y[1] (numeric) 0.24999993750001562 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 2.0000002499999843 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.0000050000382603 Order of pole (three term test) 2.0000175001899265 Radius of convergence (six term test) for eq 1 1.9999999992214055 Order of pole (six term test) 1.0000000000093872 TOP MAIN SOLVE Loop x[1] -1.99 y[1] (analytic) 0.25251881202019844 y[1] (numeric) 0.2525188120201985 absolute error 5.551115123125783e-17 relative error 2.198297655020554e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9900002512562656 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9900050251644572 Order of pole (three term test) 2.000017676515025 Radius of convergence (six term test) for eq 1 1.9900002178638694 Order of pole (six term test) 1.0000000000010107 TOP MAIN SOLVE Loop x[1] -1.98 y[1] (analytic) 0.2550759475880146 y[1] (numeric) 0.2550759475880146 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9800002525252365 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9800050505444748 Order of pole (three term test) 2.0000178555185504 Radius of convergence (six term test) for eq 1 1.980000310564718 Order of pole (six term test) 0.999999999998062 TOP MAIN SOLVE Loop x[1] -1.97 y[1] (analytic) 0.25767212304565357 y[1] (numeric) 0.25767212304565357 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9700002538070902 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9700050761821726 Order of pole (three term test) 2.0000180372550864 Radius of convergence (six term test) for eq 1 1.9700000719127866 Order of pole (six term test) 1.0000000000062501 TOP MAIN SOLVE Loop x[1] -1.96 y[1] (analytic) 0.26030813715427503 y[1] (numeric) 0.260308137154275 absolute error 5.551115123125783e-17 relative error 2.1325169408115127e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9600002551020241 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9600051020814548 Order of pole (three term test) 2.0000182217802003 Radius of convergence (six term test) for eq 1 1.9600000351835585 Order of pole (six term test) 1.0000000000079208 TOP MAIN SOLVE Loop x[1] -1.95 y[1] (analytic) 0.2629848092084657 y[1] (numeric) 0.2629848092084657 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9500002564102394 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9500051282464002 Order of pole (three term test) 2.000018409151611 Radius of convergence (six term test) for eq 1 1.950000059037856 Order of pole (six term test) 1.0000000000077458 TOP MAIN SOLVE Loop x[1] -1.94 y[1] (analytic) 0.26570297967292494 y[1] (numeric) 0.26570297967292494 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9400002577319417 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9400051546811024 Order of pole (three term test) 2.000018599428125 Radius of convergence (six term test) for eq 1 1.940000355169227 Order of pole (six term test) 0.9999999999960476 TOP MAIN SOLVE Loop x[1] -1.93 y[1] (analytic) 0.2684635108423016 y[1] (numeric) 0.2684635108423016 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9300002590673402 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9300051813897086 Order of pole (three term test) 2.000018792669762 Radius of convergence (six term test) for eq 1 1.9300000137448998 Order of pole (six term test) 1.0000000000094307 TOP MAIN SOLVE Loop x[1] -1.92 y[1] (analytic) 0.2712672875251499 y[1] (numeric) 0.2712672875251499 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.920000260416649 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.920005208376575 Order of pole (three term test) 2.0000189889388515 Radius of convergence (six term test) for eq 1 1.9200000806532336 Order of pole (six term test) 1.0000000000063523 TOP MAIN SOLVE Loop x[1] -1.91 y[1] (analytic) 0.2741152177530172 y[1] (numeric) 0.2741152177530173 absolute error 5.551115123125783e-17 relative error 2.0251028631790293e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9100002617800869 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9100052356460224 Order of pole (three term test) 2.0000191882988574 Radius of convergence (six term test) for eq 1 1.9100002336807842 Order of pole (six term test) 1.000000000001192 TOP MAIN SOLVE Loop x[1] -1.9 y[1] (analytic) 0.2770082335157248 y[1] (numeric) 0.2770082335157248 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.9000002631578765 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9000052632025115 Order of pole (three term test) 2.0000193908148405 Radius of convergence (six term test) for eq 1 1.8999998013566646 Order of pole (six term test) 1.0000000000185523 TOP MAIN SOLVE Loop x[1] -1.89 y[1] (analytic) 0.27994729152395187 y[1] (numeric) 0.27994729152395187 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.890000264550246 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8900052910506229 Order of pole (three term test) 2.0000195965540195 Radius of convergence (six term test) for eq 1 1.890000177635082 Order of pole (six term test) 1.0000000000028395 TOP MAIN SOLVE Loop x[1] -1.88 y[1] (analytic) 0.2829333740002903 y[1] (numeric) 0.2829333740002903 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.880000265957428 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.880005319194992 Order of pole (three term test) 2.0000198055850626 Radius of convergence (six term test) for eq 1 1.8799999602786601 Order of pole (six term test) 1.0000000000138174 TOP MAIN SOLVE Loop x[1] -1.8699999999999999 y[1] (analytic) 0.28596748949998874 y[1] (numeric) 0.2859674894999887 absolute error 5.551115123125783e-17 relative error 1.941170002517367e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.87000026737966 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.870005347640386 Order of pole (three term test) 2.000020017978488 Radius of convergence (six term test) for eq 1 1.8700000822487235 Order of pole (six term test) 1.0000000000080922 TOP MAIN SOLVE Loop x[1] -1.8599999999999999 y[1] (analytic) 0.289050673762668 y[1] (numeric) 0.28905067376266796 absolute error 5.551115123125783e-17 relative error 1.9204643431081082e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8600002688171848 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8600053763916455 Order of pole (three term test) 2.000020233806928 Radius of convergence (six term test) for eq 1 1.8600002429814047 Order of pole (six term test) 1.0000000000012035 TOP MAIN SOLVE Loop x[1] -1.8499999999999999 y[1] (analytic) 0.2921839905963505 y[1] (numeric) 0.2921839905963504 absolute error 5.551115123125783e-17 relative error 1.8998697060013113e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8500002702702505 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8500054054537347 Order of pole (three term test) 2.000020453144671 Radius of convergence (six term test) for eq 1 1.8500001448413528 Order of pole (six term test) 1.000000000004702 TOP MAIN SOLVE Loop x[1] -1.8399999999999999 y[1] (analytic) 0.2953685327952113 y[1] (numeric) 0.29536853279521125 absolute error 5.551115123125783e-17 relative error 1.879386091196977e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8400002717391102 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8400054348317314 Order of pole (three term test) 2.0000206760685164 Radius of convergence (six term test) for eq 1 1.8399999082615153 Order of pole (six term test) 1.0000000000165743 TOP MAIN SOLVE Loop x[1] -1.8299999999999998 y[1] (analytic) 0.29860542309253096 y[1] (numeric) 0.29860542309253096 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8300002732240233 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8300054645308086 Order of pole (three term test) 2.000020902656768 Radius of convergence (six term test) for eq 1 1.8300001182234709 Order of pole (six term test) 1.0000000000065308 TOP MAIN SOLVE Loop x[1] -1.8199999999999998 y[1] (analytic) 0.30189581515040004 y[1] (numeric) 0.3018958151504 absolute error 5.551115123125783e-17 relative error 1.8387519284956962e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.820000274725254 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8200054945562676 Order of pole (three term test) 2.0000211329904487 Radius of convergence (six term test) for eq 1 1.8200002661281636 Order of pole (six term test) 1.0000000000011076 TOP MAIN SOLVE Loop x[1] -1.8099999999999998 y[1] (analytic) 0.30524089458780423 y[1] (numeric) 0.30524089458780423 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8100002762430727 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8100055249134832 Order of pole (three term test) 2.0000213671522107 Radius of convergence (six term test) for eq 1 1.8100002241450646 Order of pole (six term test) 1.0000000000022142 TOP MAIN SOLVE Loop x[1] -1.7999999999999998 y[1] (analytic) 0.3086418800488025 y[1] (numeric) 0.30864188004880244 absolute error 5.551115123125783e-17 relative error 1.7985618550042658e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.8000002777777562 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8000055556080405 Order of pole (three term test) 2.0000216052277913 Radius of convergence (six term test) for eq 1 1.7999999535110667 Order of pole (six term test) 1.000000000014519 TOP MAIN SOLVE Loop x[1] -1.7899999999999998 y[1] (analytic) 0.31210002431259193 y[1] (numeric) 0.3121000243125919 absolute error 5.551115123125783e-17 relative error 1.778633351712244e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.790000279329587 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7900055866455402 Order of pole (three term test) 2.0000218473045144 Radius of convergence (six term test) for eq 1 1.7900001870176814 Order of pole (six term test) 1.0000000000042784 TOP MAIN SOLVE Loop x[1] -1.7799999999999998 y[1] (analytic) 0.3156166154473503 y[1] (numeric) 0.31561661544735026 absolute error 5.551115123125783e-17 relative error 1.758815870722685e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.780000280898854 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7800056180317905 Order of pole (three term test) 2.0000220934727304 Radius of convergence (six term test) for eq 1 1.7800002798023082 Order of pole (six term test) 0.9999999999996056 TOP MAIN SOLVE Loop x[1] -1.7699999999999998 y[1] (analytic) 0.3191929780098382 y[1] (numeric) 0.31919297800983815 absolute error 5.551115123125783e-17 relative error 1.7391094120355884e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.770000282485853 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7700056497727055 Order of pole (three term test) 2.0000223438251714 Radius of convergence (six term test) for eq 1 1.77000029195362 Order of pole (six term test) 0.9999999999997629 TOP MAIN SOLVE Loop x[1] -1.7599999999999998 y[1] (analytic) 0.32283047429284795 y[1] (numeric) 0.3228304742928479 absolute error 5.551115123125783e-17 relative error 1.7195139756509546e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.7600002840908862 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7600056818743204 Order of pole (three term test) 2.0000225984571776 Radius of convergence (six term test) for eq 1 1.7600000083304839 Order of pole (six term test) 1.0000000000139835 TOP MAIN SOLVE Loop x[1] -1.7499999999999998 y[1] (analytic) 0.32653050562269215 y[1] (numeric) 0.32653050562269204 absolute error 1.1102230246251565e-16 relative error 3.4000591231375656e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.7500002857142622 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7500057143428156 Order of pole (three term test) 2.0000228574668224 Radius of convergence (six term test) for eq 1 1.7500002501800511 Order of pole (six term test) 1.0000000000015126 TOP MAIN SOLVE Loop x[1] -1.7399999999999998 y[1] (analytic) 0.330294513709039 y[1] (numeric) 0.33029451370903895 absolute error 5.551115123125783e-17 relative error 1.680656169789074e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.7400002873562979 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7400057471845334 Order of pole (three term test) 2.0000231209551176 Radius of convergence (six term test) for eq 1 1.7400001467802264 Order of pole (six term test) 1.0000000000077787 TOP MAIN SOLVE Loop x[1] -1.7299999999999998 y[1] (analytic) 0.33412398204952326 y[1] (numeric) 0.3341239820495232 absolute error 5.551115123125783e-17 relative error 1.6613938003118275e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.7300002890173167 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.730005780405931 Order of pole (three term test) 2.000023389025756 Radius of convergence (six term test) for eq 1 1.7300001455344725 Order of pole (six term test) 1.0000000000074465 TOP MAIN SOLVE Loop x[1] -1.7199999999999998 y[1] (analytic) 0.33802043739168564 y[1] (numeric) 0.3380204373916856 absolute error 5.551115123125783e-17 relative error 1.6422424531370436e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.7200002906976497 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7200058140136256 Order of pole (three term test) 2.000023661785714 Radius of convergence (six term test) for eq 1 1.7200002704197541 Order of pole (six term test) 1.0000000000008091 TOP MAIN SOLVE Loop x[1] -1.7099999999999997 y[1] (analytic) 0.3419854512549328 y[1] (numeric) 0.34198545125493274 absolute error 5.551115123125783e-17 relative error 1.623202128264722e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.7100002923976356 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7100058480144251 Order of pole (three term test) 2.0000239393451436 Radius of convergence (six term test) for eq 1 1.7100001287301154 Order of pole (six term test) 1.0000000000094191 TOP MAIN SOLVE Loop x[1] -1.6999999999999997 y[1] (analytic) 0.34602064151534906 y[1] (numeric) 0.346020641515349 absolute error 5.551115123125783e-17 relative error 1.604272825694863e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.7000002941176213 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7000058824152275 Order of pole (three term test) 2.000024221817048 Radius of convergence (six term test) for eq 1 1.7000004039760144 Order of pole (six term test) 0.9999999999933138 TOP MAIN SOLVE Loop x[1] -1.6899999999999997 y[1] (analytic) 0.3501276740563447 y[1] (numeric) 0.3501276740563447 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.690000295857962 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6900059172231547 Order of pole (three term test) 2.0000245093181803 Radius of convergence (six term test) for eq 1 1.6900003796657836 Order of pole (six term test) 0.9999999999944071 TOP MAIN SOLVE Loop x[1] -1.6799999999999997 y[1] (analytic) 0.35430826448828506 y[1] (numeric) 0.35430826448828506 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.6800002976190211 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.680005952445486 Order of pole (three term test) 2.000024801968708 Radius of convergence (six term test) for eq 1 1.680000174550161 Order of pole (six term test) 1.0000000000063975 TOP MAIN SOLVE Loop x[1] -1.6699999999999997 y[1] (analytic) 0.3585641799404139 y[1] (numeric) 0.3585641799404139 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.6700002994011705 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.670005988089663 Order of pole (three term test) 2.000025099892248 Radius of convergence (six term test) for eq 1 1.6700004251916423 Order of pole (six term test) 0.9999999999925349 TOP MAIN SOLVE Loop x[1] -1.6599999999999997 y[1] (analytic) 0.36289724092856707 y[1] (numeric) 0.362897240928567 absolute error 5.551115123125783e-17 relative error 1.5296658384400526e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.6600003012047917 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6600060241632972 Order of pole (three term test) 2.0000254032162856 Radius of convergence (six term test) for eq 1 1.6600003284821787 Order of pole (six term test) 0.9999999999984794 TOP MAIN SOLVE Loop x[1] -1.6499999999999997 y[1] (analytic) 0.3673093233023607 y[1] (numeric) 0.36730932330236066 absolute error 5.551115123125783e-17 relative error 1.5112916473825062e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.6500003030302748 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6500060606741822 Order of pole (three term test) 2.0000257120720293 Radius of convergence (six term test) for eq 1 1.6500001861147249 Order of pole (six term test) 1.0000000000071596 TOP MAIN SOLVE Loop x[1] -1.6399999999999997 y[1] (analytic) 0.3718023602757436 y[1] (numeric) 0.3718023602757436 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.6400003048780203 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.640006097630349 Order of pole (three term test) 2.0000260265948486 Radius of convergence (six term test) for eq 1 1.6400002131683353 Order of pole (six term test) 1.0000000000059526 TOP MAIN SOLVE Loop x[1] -1.6299999999999997 y[1] (analytic) 0.37637834454501706 y[1] (numeric) 0.376378344545017 absolute error 5.551115123125783e-17 relative error 1.474876332174801e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.6300003067484372 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6300061350399817 Order of pole (three term test) 2.0000263469244275 Radius of convergence (six term test) for eq 1 1.630000248107934 Order of pole (six term test) 1.0000000000035607 TOP MAIN SOLVE Loop x[1] -1.6199999999999997 y[1] (analytic) 0.3810393304986549 y[1] (numeric) 0.38103933049865485 absolute error 5.551115123125783e-17 relative error 1.456835208024642e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.6200003086419457 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6200061729114774 Order of pole (three term test) 2.0000266732043723 Radius of convergence (six term test) for eq 1 1.620000217862982 Order of pole (six term test) 1.000000000005926 TOP MAIN SOLVE Loop x[1] -1.6099999999999997 y[1] (analytic) 0.3857874365234998 y[1] (numeric) 0.3857874365234998 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.610000310558976 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.610006211253452 Order of pole (three term test) 2.0000270055831115 Radius of convergence (six term test) for eq 1 1.610000289907204 Order of pole (six term test) 1.0000000000019398 TOP MAIN SOLVE Loop x[1] -1.5999999999999996 y[1] (analytic) 0.39062484741216913 y[1] (numeric) 0.39062484741216913 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.600000312499969 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6000062500747156 Order of pole (three term test) 2.0000273442135916 Radius of convergence (six term test) for eq 1 1.6000003456842948 Order of pole (six term test) 0.9999999999982432 TOP MAIN SOLVE Loop x[1] -1.5899999999999996 y[1] (analytic) 0.39555381687677843 y[1] (numeric) 0.39555381687677843 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.5900003144653774 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5900062893843092 Order of pole (three term test) 2.000027689253523 Radius of convergence (six term test) for eq 1 1.5900001813886193 Order of pole (six term test) 1.0000000000092966 TOP MAIN SOLVE Loop x[1] -1.5799999999999996 y[1] (analytic) 0.40057667017438325 y[1] (numeric) 0.4005766701743832 absolute error 5.551115123125783e-17 relative error 1.385780934448632e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.5800003164556642 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5800063291915085 Order of pole (three term test) 2.0000280408656823 Radius of convergence (six term test) for eq 1 1.5800003450686253 Order of pole (six term test) 0.9999999999981108 TOP MAIN SOLVE Loop x[1] -1.5699999999999996 y[1] (analytic) 0.40569580684984935 y[1] (numeric) 0.4056958068498493 absolute error 5.551115123125783e-17 relative error 1.3682949218107858e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.570000318471305 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5700063695058362 Order of pole (three term test) 2.000028399218125 Radius of convergence (six term test) for eq 1 1.5700000659081852 Order of pole (six term test) 1.0000000000181464 TOP MAIN SOLVE Loop x[1] -1.5599999999999996 y[1] (analytic) 0.410913703602193 y[1] (numeric) 0.410913703602193 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.5600003205127873 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5600064103370148 Order of pole (three term test) 2.000028764484051 Radius of convergence (six term test) for eq 1 1.560000260739296 Order of pole (six term test) 1.0000000000041318 TOP MAIN SOLVE Loop x[1] -1.5499999999999996 y[1] (analytic) 0.4162329172807838 y[1] (numeric) 0.4162329172807838 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.5500003225806114 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5500064516950767 Order of pole (three term test) 2.000029136842672 Radius of convergence (six term test) for eq 1 1.5500002646843203 Order of pole (six term test) 1.0000000000041238 TOP MAIN SOLVE Loop x[1] -1.5399999999999996 y[1] (analytic) 0.42165608801817867 y[1] (numeric) 0.4216560880181786 absolute error 5.551115123125783e-17 relative error 1.3165030177120221e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.54000032467529 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5400064935902813 Order of pole (three term test) 2.0000295164788033 Radius of convergence (six term test) for eq 1 1.5400004129320153 Order of pole (six term test) 0.9999999999934808 TOP MAIN SOLVE Loop x[1] -1.5299999999999996 y[1] (analytic) 0.42718594250675296 y[1] (numeric) 0.4271859425067529 absolute error 5.551115123125783e-17 relative error 1.2994610942840262e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.5300003267973503 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5300065360331534 Order of pole (three term test) 2.0000299035832216 Radius of convergence (six term test) for eq 1 1.530000269774149 Order of pole (six term test) 1.0000000000041664 TOP MAIN SOLVE Loop x[1] -1.5199999999999996 y[1] (analytic) 0.432825297426724 y[1] (numeric) 0.43282529742672393 absolute error 5.551115123125783e-17 relative error 1.2825301931584925e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.5200003289473325 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5200065790345154 Order of pole (three term test) 2.000030298353191 Radius of convergence (six term test) for eq 1 1.5200002269152715 Order of pole (six term test) 1.0000000000079945 TOP MAIN SOLVE Loop x[1] -1.5099999999999996 y[1] (analytic) 0.43857706303361144 y[1] (numeric) 0.43857706303361144 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.510000331125791 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5100066226054543 Order of pole (three term test) 2.000030700992386 Radius of convergence (six term test) for eq 1 1.510000460461359 Order of pole (six term test) 0.9999999999900107 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations 50 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 10 Minutes 0.0 Seconds Percent Done 102.00000000000009%