##############ECHO OF PROBLEM################# ##############temp/lin_arcsin_2postode.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(-0.999); x_end=c(0.999); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(6.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.0000001); glob_lower_ratio_limit=c(0.9999999); glob_look_poles=false; glob_h=c(0.0001); /* 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] = -0.999 y[1] (closed_form) = 1.569102849109797 y[1] (numeric) = 1.569102849109797 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.899000000000011 y[1] (closed_form) = 1.442452096950967 y[1] (numeric) = 1.442452096245956 absolute error = 7.050111605622078e-10 relative error = 4.887588031882996e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.799000000000022 y[1] (closed_form) = 1.34081715717502 y[1] (numeric) = 1.340817156103812 absolute error = 1.071208677316804e-09 relative error = 7.989222628786634e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.699000000000033 y[1] (closed_form) = 1.256068999979312 y[1] (numeric) = 1.256068999348898 absolute error = 6.30413943270014e-10 relative error = 5.018943571415241e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.5990000000000441 y[1] (closed_form) = 1.185393570046685 y[1] (numeric) = 1.185393569665389 absolute error = 3.812967719341032e-10 relative error = 3.216625950814684e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.4990000000000551 y[1] (closed_form) = 1.127249531353705 y[1] (numeric) = 1.127249531130516 absolute error = 2.2318880077421e-10 relative error = 1.979941393332711e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.3990000000000661 y[1] (closed_form) = 1.080669868881501 y[1] (numeric) = 1.080669868763879 absolute error = 1.176221342547024e-10 relative error = 1.088418745092263e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.2990000000000771 y[1] (closed_form) = 1.045012469837926 y[1] (numeric) = 1.045012469791328 absolute error = 4.65976146557523e-11 relative error = 4.459048671733004e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.1990000000000881 y[1] (closed_form) = 1.01984660498693 y[1] (numeric) = 1.019846604986195 absolute error = 7.349676423018536e-13 relative error = 7.206648908845197e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09900000000009551 y[1] (closed_form) = 1.00489460308493 y[1] (numeric) = 1.004894603109965 absolute error = 2.503575124990221e-11 relative error = 2.491380804817228e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0009999999999062937 y[1] (closed_form) = 1.000000605000061 y[1] (numeric) = 1.000000605033311 absolute error = 3.324984731989389e-11 relative error = 3.32498272037464e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.1009999999999081 y[1] (closed_form) = 1.005114971456507 y[1] (numeric) = 1.005114971481178 absolute error = 2.467182014243008e-11 relative error = 2.454626668895229e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.2009999999999005 y[1] (closed_form) = 1.020289592506967 y[1] (numeric) = 1.020289592505473 absolute error = 1.494360191145461e-12 relative error = 1.464643177897805e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.3009999999998895 y[1] (closed_form) = 1.045682793830028 y[1] (numeric) = 1.045682793782191 absolute error = 4.783728968504875e-11 relative error = 4.574741974077515e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.4009999999998785 y[1] (closed_form) = 1.081575206173287 y[1] (numeric) = 1.081575206053802 absolute error = 1.194846444008135e-10 relative error = 1.104728027407e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.5009999999998674 y[1] (closed_form) = 1.128401449001458 y[1] (numeric) = 1.12840144877551 absolute error = 2.259481490796134e-10 relative error = 2.002373794180775e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.6009999999998564 y[1] (closed_form) = 1.186809273005832 y[1] (numeric) = 1.186809272620337 absolute error = 3.854956354132355e-10 relative error = 3.248168380390983e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.7009999999998454 y[1] (closed_form) = 1.25777487532442 y[1] (numeric) = 1.257774874687113 absolute error = 6.37306207806887e-10 relative error = 5.066933839352656e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.8009999999998344 y[1] (closed_form) = 1.34285720829767 y[1] (numeric) = 1.342857207222862 absolute error = 1.074807576273429e-09 relative error = 8.003885816243668e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.9009999999998234 y[1] (closed_form) = 1.444915594705218 y[1] (numeric) = 1.444915594007975 absolute error = 6.972438182373253e-10 relative error = 4.825498602079744e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 Finished! diff ( y , x , 1 ) = arcsin ( x + 0.0001 ) ; Iterations = 19981 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 6 Minutes 0.0 Seconds Percent Done = 100 %