##############ECHO OF PROBLEM################# ##############temp/lin_arcsin_0d2_0d5postode.ode################# diff ( y , x , 1 ) = arcsin ( x + 0.0001 ) ; ! // BEGIN FIRST INPUT BLOCK max_terms=30; Digits=32; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.2); x_end=c(0.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_display_interval=0.0001; 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(0.0001)) * arcsin(c(x) + c(0.0001)) + sqrt(c(1.0) - (c(x) + c(0.0001)) * (c(x) +c(0.0001)))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 1.020087622166556 y[1] (numeric) = 1.020087622166556 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] = 0.21 y[1] (closed_form) = 1.022153290063964 y[1] (numeric) = 1.022153289699857 absolute error = 3.641074108884368e-10 relative error = 3.562160533334993e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = 1.024321241942537 y[1] (numeric) = 1.024321241194025 absolute error = 7.485125852468855e-10 relative error = 7.307400789886928e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = 1.02659170877264 y[1] (numeric) = 1.026591707619033 absolute error = 1.153607875892249e-09 relative error = 1.123726079252544e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = 1.028964933945962 y[1] (numeric) = 1.028964932366151 absolute error = 1.579811170770995e-09 relative error = 1.535340144889682e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 1.031441173526912 y[1] (numeric) = 1.031441171499344 absolute error = 2.027568113405209e-09 relative error = 1.965762241652754e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 1.034020696520487 y[1] (numeric) = 1.034020694023134 absolute error = 2.497353435160221e-09 relative error = 2.415187088192621e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 1.036703785157438 y[1] (numeric) = 1.036703782167767 absolute error = 2.98967162137842e-09 relative error = 2.883824351933273e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 1.039490735197639 y[1] (numeric) = 1.039490731692579 absolute error = 3.505059575914515e-09 relative error = 3.37190073680464e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 1.042381856252636 y[1] (numeric) = 1.042381852208549 absolute error = 4.044086843180139e-09 relative error = 3.879659664951034e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000001 y[1] (closed_form) = 1.045377472128448 y[1] (numeric) = 1.045377467521089 absolute error = 4.607359382902132e-09 relative error = 4.407364330820412e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000001 y[1] (closed_form) = 1.048477921189756 y[1] (numeric) = 1.048477915994234 absolute error = 5.195521568523986e-09 relative error = 4.955298975326434e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000001 y[1] (closed_form) = 1.051683556746739 y[1] (numeric) = 1.051683550937482 absolute error = 5.809256409250452e-09 relative error = 5.523768411118562e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000001 y[1] (closed_form) = 1.054994747465923 y[1] (numeric) = 1.054994741016633 absolute error = 6.449289990939633e-09 relative error = 6.113101516790205e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000001 y[1] (closed_form) = 1.058411877806498 y[1] (numeric) = 1.058411870690105 absolute error = 7.116393252459829e-09 relative error = 6.723652107162829e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000001 y[1] (closed_form) = 1.061935348483729 y[1] (numeric) = 1.061935340672344 absolute error = 7.8113848722694e-09 relative error = 7.355800787140938e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 1.065565576961187 y[1] (numeric) = 1.065565568426052 absolute error = 8.535135043175046e-09 relative error = 8.009957554668583e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 1.069302997973717 y[1] (numeric) = 1.069302988685149 absolute error = 9.288568358911675e-09 relative error = 8.686563468458528e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 1.073148064083205 y[1] (numeric) = 1.073148054010538 absolute error = 1.007266758890069e-08 relative error = 9.386093052784666e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 1.077101246269406 y[1] (numeric) = 1.077101235380928 absolute error = 1.088847745300825e-08 relative error = 1.010905659121743e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 1.081163034558304 y[1] (numeric) = 1.081163022821193 absolute error = 1.173711106083886e-08 relative error = 1.085600477048673e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000002 y[1] (closed_form) = 1.085333938690706 y[1] (numeric) = 1.085333926070955 absolute error = 1.261975146604755e-08 relative error = 1.162752864917446e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000002 y[1] (closed_form) = 1.089614488834023 y[1] (numeric) = 1.089614475296361 absolute error = 1.353766121425792e-08 relative error = 1.242426688795625e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000002 y[1] (closed_form) = 1.094005236340474 y[1] (numeric) = 1.094005221848291 absolute error = 1.449218323124057e-08 relative error = 1.324690481347051e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000002 y[1] (closed_form) = 1.098506754555292 y[1] (numeric) = 1.09850673907054 absolute error = 1.548475192514331e-08 relative error = 1.40961827143357e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000002 y[1] (closed_form) = 1.103119639678806 y[1] (numeric) = 1.103119623161908 absolute error = 1.65168980714725e-08 relative error = 1.497289820375395e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000002 y[1] (closed_form) = 1.107844511686749 y[1] (numeric) = 1.107844494096492 absolute error = 1.759025680669879e-08 relative error = 1.587791122412724e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 1.112682015313498 y[1] (numeric) = 1.112681996606922 absolute error = 1.870657673208598e-08 relative error = 1.681214980976878e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = 1.117632821103523 y[1] (numeric) = 1.117632801235794 absolute error = 1.986772946160897e-08 relative error = 1.777661597481726e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 1.12269762653682 y[1] (numeric) = 1.1226976054611 absolute error = 2.107572050213946e-08 relative error = 1.877239249819351e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 Finished! diff ( y , x , 1 ) = arcsin ( x + 0.0001 ) ; Iterations = 300 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.3 %