##############ECHO OF PROBLEM################# ##############temp/arcsin_sin_m0d5_0d5postode.ode################# diff ( y , x , 1 ) = arcsin ( sin ( x ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-0.5); x_end=c(0.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_display_interval=0.001; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(x)*c(x)/c(2.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (closed_form) = 0.125 y[1] (numeric) = 0.125 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (closed_form) = 0.12005 y[1] (numeric) = 0.1200500009003825 absolute error = 9.00382490787166e-10 relative error = 7.500062397227539e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (closed_form) = 0.1152 y[1] (numeric) = 0.1152000017793445 absolute error = 1.77934449119288e-09 relative error = 1.544569870827153e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.47 y[1] (closed_form) = 0.11045 y[1] (numeric) = 0.1104500026371109 absolute error = 2.63711087689078e-09 relative error = 2.387606045170467e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (closed_form) = 0.1058 y[1] (numeric) = 0.1058000034738988 absolute error = 3.473898863015634e-09 relative error = 3.283458282623473e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (closed_form) = 0.10125 y[1] (numeric) = 0.1012500042899181 absolute error = 4.289918115185642e-09 relative error = 4.236956163146315e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4399999999999999 y[1] (closed_form) = 0.09679999999999998 y[1] (numeric) = 0.09680000508537114 absolute error = 5.085371151958284e-09 relative error = 5.253482594998228e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4299999999999999 y[1] (closed_form) = 0.09244999999999998 y[1] (numeric) = 0.09245000586045347 absolute error = 5.860453497485985e-09 relative error = 6.339051917237411e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4199999999999999 y[1] (closed_form) = 0.08819999999999997 y[1] (numeric) = 0.08820000661535378 absolute error = 6.615353806416202e-09 relative error = 7.500401141061456e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4099999999999999 y[1] (closed_form) = 0.08404999999999997 y[1] (numeric) = 0.08405000735025416 absolute error = 7.350254183080551e-09 relative error = 8.745097183914995e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3999999999999999 y[1] (closed_form) = 0.07999999999999996 y[1] (numeric) = 0.08000000806533032 absolute error = 8.065330361906042e-09 relative error = 1.008166295238256e-05 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3899999999999999 y[1] (closed_form) = 0.07604999999999996 y[1] (numeric) = 0.0760500087607518 absolute error = 8.760751832315172e-09 relative error = 1.151972627523363e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3799999999999999 y[1] (closed_form) = 0.07219999999999996 y[1] (numeric) = 0.07220000943668198 absolute error = 9.436682019137166e-09 relative error = 1.307019670240605e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3699999999999999 y[1] (closed_form) = 0.06844999999999996 y[1] (numeric) = 0.06845001009327846 absolute error = 1.009327850465258e-08 relative error = 1.474547626684089e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3599999999999999 y[1] (closed_form) = 0.06479999999999995 y[1] (numeric) = 0.06480001073069309 absolute error = 1.073069313961561e-08 relative error = 1.655971163520929e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3499999999999999 y[1] (closed_form) = 0.06124999999999995 y[1] (numeric) = 0.06125001134907211 absolute error = 1.134907216121528e-08 relative error = 1.852909740606578e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3399999999999999 y[1] (closed_form) = 0.05779999999999995 y[1] (numeric) = 0.05780001194855637 absolute error = 1.194855642205894e-08 relative error = 2.067224294473867e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3299999999999998 y[1] (closed_form) = 0.05444999999999995 y[1] (numeric) = 0.05445001252928138 absolute error = 1.252928143180565e-08 relative error = 2.301061787292133e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3199999999999998 y[1] (closed_form) = 0.05119999999999995 y[1] (numeric) = 0.05120001309137755 absolute error = 1.309137760002743e-08 relative error = 2.55690968750536e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3099999999999998 y[1] (closed_form) = 0.04804999999999995 y[1] (numeric) = 0.04805001363497018 absolute error = 1.36349702362093e-08 relative error = 2.837662900355736e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2999999999999998 y[1] (closed_form) = 0.04499999999999995 y[1] (numeric) = 0.04500001416017969 absolute error = 1.416017974403827e-08 relative error = 3.146706609786286e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2899999999999998 y[1] (closed_form) = 0.04204999999999995 y[1] (numeric) = 0.04205001466712169 absolute error = 1.466712173936457e-08 relative error = 3.48801943861227e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2799999999999998 y[1] (closed_form) = 0.03919999999999994 y[1] (numeric) = 0.03920001515590703 absolute error = 1.515590708489611e-08 relative error = 3.866302827779627e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2699999999999998 y[1] (closed_form) = 0.03644999999999995 y[1] (numeric) = 0.03645001562664202 absolute error = 1.562664207060971e-08 relative error = 4.287144600990324e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2599999999999998 y[1] (closed_form) = 0.03379999999999994 y[1] (numeric) = 0.03380001607942842 absolute error = 1.607942848314003e-08 relative error = 4.757227361875758e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2499999999999998 y[1] (closed_form) = 0.03124999999999994 y[1] (numeric) = 0.03125001651436359 absolute error = 1.651436364741299e-08 relative error = 5.284596367172166e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2399999999999998 y[1] (closed_form) = 0.02879999999999994 y[1] (numeric) = 0.02880001693154055 absolute error = 1.693154061052637e-08 relative error = 5.879007156432781e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2299999999999998 y[1] (closed_form) = 0.02644999999999995 y[1] (numeric) = 0.02645001733104808 absolute error = 1.733104813134156e-08 relative error = 6.552381146064877e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2199999999999998 y[1] (closed_form) = 0.02419999999999994 y[1] (numeric) = 0.02420001771297075 absolute error = 1.771297080538359e-08 relative error = 7.319409423712244e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2099999999999997 y[1] (closed_form) = 0.02204999999999994 y[1] (numeric) = 0.02205001807738908 absolute error = 1.807738913076062e-08 relative error = 8.198362417578535e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1999999999999997 y[1] (closed_form) = 0.01999999999999995 y[1] (numeric) = 0.02000001842437952 absolute error = 1.842437957061405e-08 relative error = 9.212189785307048e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1899999999999997 y[1] (closed_form) = 0.01804999999999995 y[1] (numeric) = 0.0180500187540146 absolute error = 1.875401465373239e-08 relative error = 0.0001039003581924235 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1799999999999997 y[1] (closed_form) = 0.01619999999999995 y[1] (numeric) = 0.01620001906636292 absolute error = 1.906636296761244e-08 relative error = 0.0001176935985655092 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1699999999999997 y[1] (closed_form) = 0.01444999999999995 y[1] (numeric) = 0.01445001936148924 absolute error = 1.936148929029824e-08 relative error = 0.00013398954526158 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1599999999999997 y[1] (closed_form) = 0.01279999999999995 y[1] (numeric) = 0.01280001963945454 absolute error = 1.963945458691163e-08 relative error = 0.0001534332389602477 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1499999999999997 y[1] (closed_form) = 0.01124999999999995 y[1] (numeric) = 0.01125001990031605 absolute error = 1.990031609291898e-08 relative error = 0.000176891698603725 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1399999999999997 y[1] (closed_form) = 0.009799999999999955 y[1] (numeric) = 0.009800020144127305 absolute error = 2.014412735056037e-08 relative error = 0.0002055523199036782 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1299999999999997 y[1] (closed_form) = 0.008449999999999958 y[1] (numeric) = 0.00845002037093822 absolute error = 2.037093826262604e-08 relative error = 0.0002410761924571141 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1199999999999997 y[1] (closed_form) = 0.00719999999999996 y[1] (numeric) = 0.007200020580795079 absolute error = 2.058079511934457e-08 relative error = 0.0002858443766575651 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1099999999999997 y[1] (closed_form) = 0.006049999999999962 y[1] (numeric) = 0.006050020773740614 absolute error = 2.077374065215937e-08 relative error = 0.000343367614085281 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.09999999999999964 y[1] (closed_form) = 0.004999999999999965 y[1] (numeric) = 0.00500002094981402 absolute error = 2.094981405541263e-08 relative error = 0.0004189962811082556 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.08999999999999964 y[1] (closed_form) = 0.004049999999999967 y[1] (numeric) = 0.004050021109050997 absolute error = 2.11090510297135e-08 relative error = 0.0005212111365361401 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.07999999999999963 y[1] (closed_form) = 0.00319999999999997 y[1] (numeric) = 0.003200021251483768 absolute error = 2.125148379798422e-08 relative error = 0.0006641088686870131 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.06999999999999962 y[1] (closed_form) = 0.002449999999999973 y[1] (numeric) = 0.002450021377141119 absolute error = 2.13771411453588e-08 relative error = 0.0008725363732799604 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.05999999999999961 y[1] (closed_form) = 0.001799999999999977 y[1] (numeric) = 0.001800021486048408 absolute error = 2.148604843154288e-08 relative error = 0.001193669357307953 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.0499999999999996 y[1] (closed_form) = 0.00124999999999998 y[1] (numeric) = 0.001250021578227599 absolute error = 2.157822761878619e-08 relative error = 0.001726258209502923 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.03999999999999959 y[1] (closed_form) = 0.0007999999999999837 y[1] (numeric) = 0.0008000216536972678 absolute error = 2.165369728413403e-08 relative error = 0.002706712160516809 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.02999999999999958 y[1] (closed_form) = 0.0004499999999999875 y[1] (numeric) = 0.0004500217124726254 absolute error = 2.171247263796708e-08 relative error = 0.004824993919548374 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.01999999999999957 y[1] (closed_form) = 0.0001999999999999915 y[1] (numeric) = 0.000200021754565526 absolute error = 2.175456553451822e-08 relative error = 0.01087728276725957 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.009999999999999565 y[1] (closed_form) = 4.999999999999565e-05 y[1] (numeric) = 5.00217799844779e-05 absolute error = 2.177998448225373e-08 relative error = 0.04355996896451125 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.371503159461554e-16 y[1] (closed_form) = 9.555019936591174e-32 y[1] (numeric) = 2.178873464988079e-08 absolute error = 2.178873464988079e-08 relative error = -1 % Desired digits = 8 Estimated correct digits = 6 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.01000000000000044 y[1] (closed_form) = 5.000000000000439e-05 y[1] (numeric) = 5.002178081787549e-05 absolute error = 2.178081787109263e-08 relative error = 0.04356163574218142 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000045 y[1] (closed_form) = 0.000200000000000009 y[1] (numeric) = 0.0002000217562326546 absolute error = 2.175623264562884e-08 relative error = 0.01087811632281393 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000046 y[1] (closed_form) = 0.0004500000000000137 y[1] (numeric) = 0.000450021714974152 absolute error = 2.171497413827606e-08 relative error = 0.004825549808505643 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000047 y[1] (closed_form) = 0.0008000000000000186 y[1] (numeric) = 0.0008000216570341938 absolute error = 2.165703417522733e-08 relative error = 0.002707129271903354 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000047 y[1] (closed_form) = 0.001250000000000024 y[1] (numeric) = 0.00125002158240126 absolute error = 2.158240123683458e-08 relative error = 0.001726592098946734 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000048 y[1] (closed_form) = 0.001800000000000029 y[1] (numeric) = 0.001800021491060478 absolute error = 2.149106044903662e-08 relative error = 0.001193947802724237 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000049 y[1] (closed_form) = 0.002450000000000035 y[1] (numeric) = 0.002450021382993606 absolute error = 2.138299357154136e-08 relative error = 0.0008727752478180023 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.0800000000000005 y[1] (closed_form) = 0.00320000000000004 y[1] (numeric) = 0.003200021258179022 absolute error = 2.125817898232171e-08 relative error = 0.0006643180931975452 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000051 y[1] (closed_form) = 0.004050000000000046 y[1] (numeric) = 0.004050021116591706 absolute error = 2.111659166015994e-08 relative error = 0.000521397324942215 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000005 y[1] (closed_form) = 0.005000000000000052 y[1] (numeric) = 0.005000020958203218 absolute error = 2.095820316599939e-08 relative error = 0.0004191640633199834 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000005 y[1] (closed_form) = 0.006050000000000058 y[1] (numeric) = 0.006050020782981678 absolute error = 2.078298162039305e-08 relative error = 0.0003435203573618653 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000005 y[1] (closed_form) = 0.007200000000000064 y[1] (numeric) = 0.007200020590891738 absolute error = 2.059089167401329e-08 relative error = 0.0002859846065835154 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000005 y[1] (closed_form) = 0.008450000000000069 y[1] (numeric) = 0.008450020381894551 absolute error = 2.038189448293204e-08 relative error = 0.0002412058518690163 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000005 y[1] (closed_form) = 0.009800000000000076 y[1] (numeric) = 0.009800020155947744 absolute error = 2.015594766785478e-08 relative error = 0.0002056729353862716 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000005 y[1] (closed_form) = 0.01125000000000008 y[1] (numeric) = 0.01125001991300538 absolute error = 1.991300529677331e-08 relative error = 0.0001770044915268726 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000006 y[1] (closed_form) = 0.01280000000000009 y[1] (numeric) = 0.01280001965301792 absolute error = 1.965301783292406e-08 relative error = 0.0001535392018197181 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000006 y[1] (closed_form) = 0.0144500000000001 y[1] (numeric) = 0.01445001937593219 absolute error = 1.937593209835886e-08 relative error = 0.0001340894954903718 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000006 y[1] (closed_form) = 0.0162000000000001 y[1] (numeric) = 0.01620001908169133 absolute error = 1.908169122710746e-08 relative error = 0.0001177882174512798 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000006 y[1] (closed_form) = 0.01805000000000011 y[1] (numeric) = 0.01805001877023473 absolute error = 1.87702346235441e-08 relative error = 0.0001039902195210193 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000006 y[1] (closed_form) = 0.02000000000000012 y[1] (numeric) = 0.02000001844149803 absolute error = 1.844149790861116e-08 relative error = 9.220748954305526e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000006 y[1] (closed_form) = 0.02205000000000013 y[1] (numeric) = 0.02205001809541298 absolute error = 1.809541285910377e-08 relative error = 8.206536444037943e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000006 y[1] (closed_form) = 0.02420000000000013 y[1] (numeric) = 0.0242000177319075 absolute error = 1.773190736256702e-08 relative error = 7.327234447341705e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000006 y[1] (closed_form) = 0.02645000000000014 y[1] (numeric) = 0.02645001735090549 absolute error = 1.735090535137651e-08 relative error = 6.5598886016546e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000006 y[1] (closed_form) = 0.02880000000000015 y[1] (numeric) = 0.02880001695232687 absolute error = 1.6952326722941e-08 relative error = 5.886224556576706e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000006 y[1] (closed_form) = 0.03125000000000015 y[1] (numeric) = 0.03125001653608746 absolute error = 1.6536087305008e-08 relative error = 5.291547937602533e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000006 y[1] (closed_form) = 0.03380000000000016 y[1] (numeric) = 0.03380001610209889 absolute error = 1.610209872382473e-08 relative error = 4.763934533675933e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000006 y[1] (closed_form) = 0.03645000000000017 y[1] (numeric) = 0.03645001565026858 absolute error = 1.565026840760764e-08 relative error = 4.293626449275052e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000006 y[1] (closed_form) = 0.03920000000000018 y[1] (numeric) = 0.03920001518049962 absolute error = 1.518049944082556e-08 relative error = 3.872576387965685e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000006 y[1] (closed_form) = 0.04205000000000018 y[1] (numeric) = 0.04205001469269069 absolute error = 1.469269050174971e-08 relative error = 3.494100000416086e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000007 y[1] (closed_form) = 0.0450000000000002 y[1] (numeric) = 0.04500001418673594 absolute error = 1.418673573755358e-08 relative error = 3.152607941678559e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000007 y[1] (closed_form) = 0.0480500000000002 y[1] (numeric) = 0.04805001366252497 absolute error = 1.366252476431296e-08 relative error = 2.843397453551071e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000007 y[1] (closed_form) = 0.05120000000000022 y[1] (numeric) = 0.05120001311994266 absolute error = 1.311994243802239e-08 relative error = 2.562488757426238e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000007 y[1] (closed_form) = 0.05445000000000023 y[1] (numeric) = 0.05445001255886908 absolute error = 1.255886885459523e-08 relative error = 2.306495657409582e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000007 y[1] (closed_form) = 0.05780000000000023 y[1] (numeric) = 0.05780001197917941 absolute error = 1.197917917639124e-08 relative error = 2.072522348856608e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000007 y[1] (closed_form) = 0.06125000000000024 y[1] (numeric) = 0.06125001138074379 absolute error = 1.138074354894991e-08 relative error = 1.858080579420387e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000007 y[1] (closed_form) = 0.06480000000000026 y[1] (numeric) = 0.06480001076342716 absolute error = 1.076342689976251e-08 relative error = 1.66102266971643e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000007 y[1] (closed_form) = 0.06845000000000026 y[1] (numeric) = 0.06845001012708928 absolute error = 1.012708901459991e-08 relative error = 1.479487072987564e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000007 y[1] (closed_form) = 0.07220000000000028 y[1] (numeric) = 0.07220000947158442 absolute error = 9.47158414199567e-09 relative error = 1.311853759279174e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000007 y[1] (closed_form) = 0.07605000000000028 y[1] (numeric) = 0.07605000879676127 absolute error = 8.796760986307106e-09 relative error = 1.156707559014737e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000007 y[1] (closed_form) = 0.08000000000000029 y[1] (numeric) = 0.08000000810246288 absolute error = 8.102462589754111e-09 relative error = 1.01280782371926e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000008 y[1] (closed_form) = 0.08405000000000031 y[1] (numeric) = 0.08405000738852637 absolute error = 7.388526068741186e-09 relative error = 8.790631848591503e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000008 y[1] (closed_form) = 0.08820000000000032 y[1] (numeric) = 0.08820000665478288 absolute error = 6.654782558346284e-09 relative error = 7.545104941435669e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000008 y[1] (closed_form) = 0.09245000000000034 y[1] (numeric) = 0.09245000590105733 absolute error = 5.90105699027621e-09 relative error = 6.382971325339306e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000008 y[1] (closed_form) = 0.09680000000000034 y[1] (numeric) = 0.09680000512716826 absolute error = 5.127167912455377e-09 relative error = 5.296661066586114e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000008 y[1] (closed_form) = 0.1012500000000004 y[1] (numeric) = 0.1012500043329276 absolute error = 4.332927294736777e-09 relative error = 4.27943436517211e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000008 y[1] (closed_form) = 0.1058000000000004 y[1] (numeric) = 0.1058000035181407 absolute error = 3.518140306857376e-09 relative error = 3.32527439211471e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000008 y[1] (closed_form) = 0.1104500000000004 y[1] (numeric) = 0.1104500026826055 absolute error = 2.682605165782448e-09 relative error = 2.42879598531683e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000008 y[1] (closed_form) = 0.1152000000000004 y[1] (numeric) = 0.1152000018261133 absolute error = 1.826112927538759e-09 relative error = 1.585167471821834e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000008 y[1] (closed_form) = 0.1200500000000004 y[1] (numeric) = 0.1200500009484475 absolute error = 9.484471263920824e-10 relative error = 7.900434205681626e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 Finished! diff ( y , x , 1 ) = arcsin ( sin ( x ) ) ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %