##############ECHO OF PROBLEM################# ##############temp/sinpostode.ode################# diff ( y , x , 1 ) = sin(x); ! #BEGIN FIRST INPUT BLOCK ## Comment 1 # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ## Comment 2 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK ## Comment 3 x_start=0.1 x_end=1.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 ## Comment 4 #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 ## Comment 5 def exact_soln_y (x) ## Comment 6 return(2.0 - cos(x)) ## Comment 7 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 0.9 estimated_steps 900000.0000000001 step_error 1.111111111111111e-16 est_needed_step_err 1.111111111111111e-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 4.755599839543479e-110 estimated_step_error 4.755599839543479e-110 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 3.1166299016459704e-105 estimated_step_error 3.1166299016459704e-105 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 2.0425145602876815e-100 estimated_step_error 2.0425145602876815e-100 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 1.3385823264293503e-95 estimated_step_error 1.3385823264293503e-95 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 8.772532927382661e-91 estimated_step_error 8.772532927382661e-91 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 5.749166907831384e-86 estimated_step_error 5.749166907831384e-86 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 3.767773668906066e-81 estimated_step_error 3.767773668906066e-81 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 2.4692476852741952e-76 estimated_step_error 2.4692476852741952e-76 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 1.618245551695101e-71 estimated_step_error 1.618245551695101e-71 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 1.0605326033962544e-66 estimated_step_error 1.0605326033962544e-66 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 6.9502959637643855e-62 estimated_step_error 6.9502959637643855e-62 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 4.554932186727368e-57 estimated_step_error 4.554932186727368e-57 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 2.9851022859593317e-52 estimated_step_error 2.9851022859593317e-52 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 1.9562929066575893e-47 estimated_step_error 1.9562929066575893e-47 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 1.2820449137972158e-42 estimated_step_error 1.2820449137972158e-42 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 8.40159776610056e-38 estimated_step_error 8.40159776610056e-38 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 5.505524136524434e-33 estimated_step_error 5.505524136524434e-33 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 3.607364371667479e-28 estimated_step_error 3.607364371667479e-28 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 1.0049958347219743 y[1] (numeric) 1.0049958347219743 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 TOP MAIN SOLVE Loop x[1] 0.11 y[1] (analytic) 1.0060439020433032 y[1] (numeric) 1.0060439020433032 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 TOP MAIN SOLVE Loop x[1] 0.12 y[1] (analytic) 1.0071913641461339 y[1] (numeric) 1.0071913641461339 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 TOP MAIN SOLVE Loop x[1] 0.13 y[1] (analytic) 1.008438106285212 y[1] (numeric) 1.0084381062852121 absolute error 2.220446049250313e-16 relative error 2.201866465984492e-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 TOP MAIN SOLVE Loop x[1] 0.14 y[1] (analytic) 1.0097840037873629 y[1] (numeric) 1.009784003787363 absolute error 2.220446049250313e-16 relative error 2.1989316932355442e-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 TOP MAIN SOLVE Loop x[1] 0.15000000000000002 y[1] (analytic) 1.0112289220639576 y[1] (numeric) 1.011228922063958 absolute error 4.440892098500626e-16 relative error 4.391579395728311e-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 TOP MAIN SOLVE Loop x[1] 0.16000000000000003 y[1] (analytic) 1.0127727166243732 y[1] (numeric) 1.0127727166243734 absolute error 2.220446049250313e-16 relative error 2.1924426011901082e-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 TOP MAIN SOLVE Loop x[1] 0.17000000000000004 y[1] (analytic) 1.0144152330904395 y[1] (numeric) 1.0144152330904397 absolute error 2.220446049250313e-16 relative error 2.188892651469431e-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 TOP MAIN SOLVE Loop x[1] 0.18000000000000005 y[1] (analytic) 1.0161563072118787 y[1] (numeric) 1.0161563072118789 absolute error 2.220446049250313e-16 relative error 2.1851422202384934e-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 TOP MAIN SOLVE Loop x[1] 0.19000000000000006 y[1] (analytic) 1.0179957648827296 y[1] (numeric) 1.01799576488273 absolute error 4.440892098500626e-16 relative error 4.362387596978073e-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 TOP MAIN SOLVE Loop x[1] 0.20000000000000007 y[1] (analytic) 1.0199334221587584 y[1] (numeric) 1.0199334221587588 absolute error 4.440892098500626e-16 relative error 4.3540999853707865e-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 TOP MAIN SOLVE Loop x[1] 0.21000000000000008 y[1] (analytic) 1.0219690852758516 y[1] (numeric) 1.0219690852758523 absolute error 6.661338147750939e-16 relative error 6.51814056190643e-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 TOP MAIN SOLVE Loop x[1] 0.22000000000000008 y[1] (analytic) 1.0241025506693946 y[1] (numeric) 1.024102550669395 absolute error 4.440892098500626e-16 relative error 4.336374414454764e-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 TOP MAIN SOLVE Loop x[1] 0.2300000000000001 y[1] (analytic) 1.0263336049946252 y[1] (numeric) 1.0263336049946257 absolute error 4.440892098500626e-16 relative error 4.3269479600873856e-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 TOP MAIN SOLVE Loop x[1] 0.2400000000000001 y[1] (analytic) 1.0286620251479706 y[1] (numeric) 1.028662025147971 absolute error 4.440892098500626e-16 relative error 4.31715372973141e-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 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (analytic) 1.0310875782893554 y[1] (numeric) 1.0310875782893558 absolute error 4.440892098500626e-16 relative error 4.3069979621598864e-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 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (analytic) 1.0336100218654867 y[1] (numeric) 1.0336100218654873 absolute error 6.661338147750939e-16 relative error 6.44473061099812e-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 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (analytic) 1.0362291036341094 y[1] (numeric) 1.03622910363411 absolute error 6.661338147750939e-16 relative error 6.428441475335214e-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 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (analytic) 1.0389445616892292 y[1] (numeric) 1.0389445616892297 absolute error 4.440892098500626e-16 relative error 4.274426434534813e-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 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (analytic) 1.041756124487303 y[1] (numeric) 1.0417561244873035 absolute error 4.440892098500626e-16 relative error 4.262890319638099e-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 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (analytic) 1.044663510874394 y[1] (numeric) 1.0446635108743947 absolute error 6.661338147750939e-16 relative error 6.376539506175851e-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 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (analytic) 1.0476664301142866 y[1] (numeric) 1.0476664301142873 absolute error 6.661338147750939e-16 relative error 6.358262473890926e-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 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (analytic) 1.050764581917559 y[1] (numeric) 1.0507645819175597 absolute error 6.661338147750939e-16 relative error 6.339515303793875e-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 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (analytic) 1.053957656471613 y[1] (numeric) 1.0539576564716135 absolute error 4.440892098500626e-16 relative error 4.2135393876900364e-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 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (analytic) 1.057245334471654 y[1] (numeric) 1.0572453344716544 absolute error 4.440892098500626e-16 relative error 4.200436694970057e-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 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (analytic) 1.060627287152621 y[1] (numeric) 1.0606272871526217 absolute error 6.661338147750939e-16 relative error 6.280564556880378e-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 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (analytic) 1.0641031763220652 y[1] (numeric) 1.0641031763220656 absolute error 4.440892098500626e-16 relative error 4.173366077009557e-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 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (analytic) 1.0676726543939656 y[1] (numeric) 1.067672654393966 absolute error 4.440892098500626e-16 relative error 4.159413543303096e-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 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (analytic) 1.07133536442349 y[1] (numeric) 1.0713353644234902 absolute error 2.220446049250313e-16 relative error 2.0725966144552558e-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 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (analytic) 1.0750909401426871 y[1] (numeric) 1.0750909401426874 absolute error 2.220446049250313e-16 relative error 2.0653564887781615e-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 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (analytic) 1.078939005997115 y[1] (numeric) 1.0789390059971153 absolute error 4.440892098500626e-16 relative error 4.1159806752899073e-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 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (analytic) 1.082879177183395 y[1] (numeric) 1.0828791771833952 absolute error 2.220446049250313e-16 relative error 2.050502120675889e-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 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (analytic) 1.0869110596876919 y[1] (numeric) 1.086911059687692 absolute error 2.220446049250313e-16 relative error 2.0428958096059175e-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 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (analytic) 1.091034250325115 y[1] (numeric) 1.0910342503251151 absolute error 2.220446049250313e-16 relative error 2.0351753838971117e-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 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (analytic) 1.0952483367800367 y[1] (numeric) 1.0952483367800367 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 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (analytic) 1.0995528976473232 y[1] (numeric) 1.0995528976473232 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 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (analytic) 1.103947502474475 y[1] (numeric) 1.103947502474475 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 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (analytic) 1.1084317118046711 y[1] (numeric) 1.1084317118046711 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 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (analytic) 1.1130050772207158 y[1] (numeric) 1.1130050772207158 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 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (analytic) 1.1176671413898787 y[1] (numeric) 1.1176671413898784 absolute error 2.220446049250313e-16 relative error 1.9866791883038362e-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 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y[1] (analytic) 1.1224174381096275 y[1] (numeric) 1.1224174381096272 absolute error 2.220446049250313e-16 relative error 1.9782711617435154e-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 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (analytic) 1.1272554923542488 y[1] (numeric) 1.1272554923542486 absolute error 2.220446049250313e-16 relative error 1.9697806436169668e-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 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (analytic) 1.1321808203223502 y[1] (numeric) 1.13218082032235 absolute error 2.220446049250313e-16 relative error 1.9612115038462815e-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 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (analytic) 1.1371929294852392 y[1] (numeric) 1.137192929485239 absolute error 2.220446049250313e-16 relative error 1.952567582578462e-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 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y[1] (analytic) 1.142291318636176 y[1] (numeric) 1.1422913186361758 absolute error 2.220446049250313e-16 relative error 1.9438526871598622e-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 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (analytic) 1.1474754779404943 y[1] (numeric) 1.1474754779404943 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 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y[1] (analytic) 1.1527448889865841 y[1] (numeric) 1.152744888986584 absolute error 2.220446049250313e-16 relative error 1.9262250220882612e-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 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (analytic) 1.1580990248377314 y[1] (numeric) 1.1580990248377312 absolute error 2.220446049250313e-16 relative error 1.9173196778759346e-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 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (analytic) 1.1635373500848134 y[1] (numeric) 1.163537350084813 absolute error 4.440892098500626e-16 relative error 3.816716410673811e-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 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (analytic) 1.1690593208998368 y[1] (numeric) 1.1690593208998363 absolute error 4.440892098500626e-16 relative error 3.7986884147867076e-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 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (analytic) 1.1746643850903218 y[1] (numeric) 1.1746643850903216 absolute error 2.220446049250313e-16 relative error 1.890281238993706e-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 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (analytic) 1.1803519821545208 y[1] (numeric) 1.1803519821545203 absolute error 4.440892098500626e-16 relative error 3.76234561015823e-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 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (analytic) 1.1861215433374663 y[1] (numeric) 1.1861215433374659 absolute error 4.440892098500626e-16 relative error 3.744044717377785e-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 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (analytic) 1.1919724916878485 y[1] (numeric) 1.191972491687848 absolute error 4.440892098500626e-16 relative error 3.725666598406366e-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 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (analytic) 1.1979042421157078 y[1] (numeric) 1.1979042421157073 absolute error 4.440892098500626e-16 relative error 3.707217941441827e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.445438222209643 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 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (analytic) 1.2039162014509444 y[1] (numeric) 1.2039162014509441 absolute error 2.220446049250313e-16 relative error 1.8443526605707772e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.602043991336768 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 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (analytic) 1.2100077685026354 y[1] (numeric) 1.210007768502635 absolute error 4.440892098500626e-16 relative error 3.670135195905525e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.7610491284366425 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 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (analytic) 1.216178334119151 y[1] (numeric) 1.2161783341191508 absolute error 2.220446049250313e-16 relative error 1.8257569527075396e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.922541747282573 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 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (analytic) 1.2224272812490724 y[1] (numeric) 1.2224272812490722 absolute error 2.220446049250313e-16 relative error 1.816423834210791e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.086613751425658 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 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (analytic) 1.2287539850028937 y[1] (numeric) 1.2287539850028935 absolute error 2.220446049250313e-16 relative error 1.8070712903894136e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.253361052690256 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 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (analytic) 1.2351578127155118 y[1] (numeric) 1.2351578127155116 absolute error 2.220446049250313e-16 relative error 1.797702306856345e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.422883804630803 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 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (analytic) 1.241638124009492 y[1] (numeric) 1.2416381240094918 absolute error 2.220446049250313e-16 relative error 1.788319806160638e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.595286652169417 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 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (analytic) 1.2481942708591054 y[1] (numeric) 1.248194270859105 absolute error 4.440892098500626e-16 relative error 3.5578532942985353e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.770678998748352 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 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (analytic) 1.2548255976551301 y[1] (numeric) 1.2548255976551295 absolute error 6.661338147750939e-16 relative error 5.308576873311208e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.949175292458152 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 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (analytic) 1.2615314412704124 y[1] (numeric) 1.261531441270412 absolute error 4.440892098500626e-16 relative error 3.520238935962207e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 9.130895332743021 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 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y[1] (analytic) 1.2683111311261794 y[1] (numeric) 1.268311131126179 absolute error 4.440892098500626e-16 relative error 3.501421685511344e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 9.315964599440733 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 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (analytic) 1.2751639892590951 y[1] (numeric) 1.2751639892590947 absolute error 4.440892098500626e-16 relative error 3.482604697048342e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 9.469184248751768 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 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (analytic) 1.282089330389057 y[1] (numeric) 1.2820893303890566 absolute error 4.440892098500626e-16 relative error 3.4637930394078026e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 9.281524146426928 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 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (analytic) 1.289086461987723 y[1] (numeric) 1.2890864619877227 absolute error 2.220446049250313e-16 relative error 1.722495825319947e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 9.097695265112282 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 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y[1] (analytic) 1.2961546843477643 y[1] (numeric) 1.296154684347764 absolute error 2.220446049250313e-16 relative error 1.713102669044212e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.917545799867986 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 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (analytic) 1.3032932906528352 y[1] (numeric) 1.3032932906528347 absolute error 4.440892098500626e-16 relative error 3.407438778631424e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.74093140585426 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 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (analytic) 1.3105015670482534 y[1] (numeric) 1.3105015670482532 absolute error 2.220446049250313e-16 relative error 1.6943482595382162e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.56771473547375 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 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (analytic) 1.317778792712387 y[1] (numeric) 1.3177787927123867 absolute error 2.220446049250313e-16 relative error 1.6849914883513676e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.397765009316926 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 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (analytic) 1.3251242399287335 y[1] (numeric) 1.3251242399287333 absolute error 2.220446049250313e-16 relative error 1.675651219971443e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.230957618057815 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 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (analytic) 1.3325371741586922 y[1] (numeric) 1.3325371741586922 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 8.067173752719086 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 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (analytic) 1.3400168541150184 y[1] (numeric) 1.3400168541150181 absolute error 2.220446049250313e-16 relative error 1.657028448882274e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.906300060968091 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 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (analytic) 1.3475625318359485 y[1] (numeric) 1.3475625318359485 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.748228327323274 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 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (analytic) 1.3551734527599995 y[1] (numeric) 1.3551734527599992 absolute error 2.220446049250313e-16 relative error 1.638495828506724e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.592855175344939 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 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (analytic) 1.3628488558014205 y[1] (numeric) 1.3628488558014202 absolute error 2.220446049250313e-16 relative error 1.6292680144230553e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.440081790059654 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 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (analytic) 1.3705879734263036 y[1] (numeric) 1.3705879734263036 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.28981365902474 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 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (analytic) 1.378390031729336 y[1] (numeric) 1.378390031729336 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 7.141960330580845 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 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (analytic) 1.386254250511189 y[1] (numeric) 1.386254250511189 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 6.99643518796825 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 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (analytic) 1.3941798433565378 y[1] (numeric) 1.3941798433565378 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 6.8531552380975995 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 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (analytic) 1.4021660177127022 y[1] (numeric) 1.4021660177127024 absolute error 2.220446049250313e-16 relative error 1.5835828434014103e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 6.712040913869643 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 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (analytic) 1.4102119749689024 y[1] (numeric) 1.4102119749689024 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 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (analytic) 1.418316910536117 y[1] (numeric) 1.418316910536117 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 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (analytic) 1.426480013927544 y[1] (numeric) 1.426480013927544 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 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (analytic) 1.4347004688396463 y[1] (numeric) 1.4347004688396463 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 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (analytic) 1.4429774532337833 y[1] (numeric) 1.4429774532337833 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 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (analytic) 1.4513101394184131 y[1] (numeric) 1.4513101394184131 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 Finished! diff ( y , x , 1 ) = sin(x); Iterations 90 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 101.11111111111119%