##############ECHO OF PROBLEM################# ##############temp/lin_arcsin_4postode.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(-0.9); x_end=c(0.89); 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] = -0.9 y[1] (closed_form) = 1.443570492370315 y[1] (numeric) = 1.443570492370315 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] = -0.800000000000011 y[1] (closed_form) = 1.341743453212216 y[1] (numeric) = 1.341743452835634 absolute error = 3.7658209883773e-10 relative error = 2.806662465437557e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.700000000000022 y[1] (closed_form) = 1.256843557733248 y[1] (numeric) = 1.256843557800411 absolute error = 6.716294187469884e-11 relative error = 5.343778981994309e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.6000000000000331 y[1] (closed_form) = 1.186036321414917 y[1] (numeric) = 1.186036321732443 absolute error = 3.175257834442391e-10 relative error = 2.677201175976105e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.5000000000000441 y[1] (closed_form) = 1.127772437479426 y[1] (numeric) = 1.127772437955728 absolute error = 4.763021088649566e-10 relative error = 4.223388451747349e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.4000000000000551 y[1] (closed_form) = 1.08108073118894 y[1] (numeric) = 1.081080731771224 absolute error = 5.82284220840279e-10 relative error = 5.386130785995051e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.3000000000000661 y[1] (closed_form) = 1.04531653359755 y[1] (numeric) = 1.045316534251149 absolute error = 6.53599174782471e-10 relative error = 6.252643613442631e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.2000000000000771 y[1] (closed_form) = 1.020047350582342 y[1] (numeric) = 1.020047351282026 absolute error = 6.996834223116366e-10 relative error = 6.859322970763948e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.1000000000000847 y[1] (closed_form) = 1.00499416750584 y[1] (numeric) = 1.004994168231479 absolute error = 7.256384382259284e-10 relative error = 7.220324870409872e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -8.282635102947744e-14 y[1] (closed_form) = 1.000000005 y[1] (numeric) = 1.000000005734022 absolute error = 7.340223984186878e-10 relative error = 7.340223947485758e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.099999999999919 y[1] (closed_form) = 1.00501420099009 y[1] (numeric) = 1.005014201715703 absolute error = 7.256126810517571e-10 relative error = 7.219924657153298e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.1999999999999115 y[1] (closed_form) = 1.020087622166538 y[1] (numeric) = 1.02008762286617 absolute error = 6.996323520525038e-10 relative error = 6.858551528804682e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.2999999999999005 y[1] (closed_form) = 1.045377472128418 y[1] (numeric) = 1.04537747278193 absolute error = 6.535116892081305e-10 relative error = 6.251442245809663e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.3999999999998894 y[1] (closed_form) = 1.081163034558258 y[1] (numeric) = 1.081163035140412 absolute error = 5.82153880657188e-10 relative error = 5.384515212315268e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.4999999999998784 y[1] (closed_form) = 1.127877157234715 y[1] (numeric) = 1.127877157710824 absolute error = 4.761087080140669e-10 relative error = 4.221281590464794e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.5999999999998674 y[1] (closed_form) = 1.18616502163696 y[1] (numeric) = 1.186165021954194 absolute error = 3.172337947887627e-10 relative error = 2.674449077506653e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.6999999999998564 y[1] (closed_form) = 1.256998637233083 y[1] (numeric) = 1.256998637299761 absolute error = 6.667799645754258e-11 relative error = 5.304540075263313e-09 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 11 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.7999999999998454 y[1] (closed_form) = 1.341928912256897 y[1] (numeric) = 1.341928911879385 absolute error = 3.77512021643156e-10 relative error = 2.813204322487133e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.0001 Finished! diff ( y , x , 1 ) = arcsin ( x + 0.0001 ) ; Iterations = 17901 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 6 Minutes 0.0 Seconds Percent Done = 100 %