##############ECHO OF PROBLEM################# ##############temp/lin_arcsinpostode.ode################# diff ( y , x , 1 ) = arcsin ( 0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-0.8); x_end=c(0.8); 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(10.0) * (c(0.1) * c(x) + c(0.2)) * arcsin(c(0.1) * c(x) + c(0.2) )+c(10.0) * sqrt(c(1.0) - expt((c(0.1) * c(x) + c(0.2)) , c(2) ))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (closed_form) = 10.07208677566643 y[1] (numeric) = 10.07208677566643 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] = -0.7000000000000111 y[1] (closed_form) = 10.08461961211218 y[1] (numeric) = 10.08461961211197 absolute error = 2.167155344068306e-13 relative error = 2.148970836208272e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.6000000000000221 y[1] (closed_form) = 10.09816101618305 y[1] (numeric) = 10.09816101618261 absolute error = 4.369837824924616e-13 relative error = 4.327360019236799e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.5000000000000331 y[1] (closed_form) = 10.11271237580762 y[1] (numeric) = 10.11271237580694 absolute error = 6.838973831690964e-13 relative error = 6.762749277880843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.4000000000000441 y[1] (closed_form) = 10.1282751881255 y[1] (numeric) = 10.12827518812457 absolute error = 9.325873406851315e-13 relative error = 9.207760683462735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.3000000000000551 y[1] (closed_form) = 10.14485106091357 y[1] (numeric) = 10.14485106091234 absolute error = 1.238120717061975e-12 relative error = 1.220442478285608e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.2000000000000661 y[1] (closed_form) = 10.16244171413012 y[1] (numeric) = 10.16244171412856 absolute error = 1.56141766183282e-12 relative error = 1.536459155934724e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.1000000000000737 y[1] (closed_form) = 10.18104898158114 y[1] (numeric) = 10.18104898157926 absolute error = 1.877609179246065e-12 relative error = 1.844219768162305e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -7.183514308568839e-14 y[1] (closed_form) = 10.20067481271336 y[1] (numeric) = 10.20067481271116 absolute error = 2.19912976717751e-12 relative error = 2.155866947583388e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.09999999999992999 y[1] (closed_form) = 10.22132127453913 y[1] (numeric) = 10.22132127453655 absolute error = 2.581046487648564e-12 relative error = 2.525159339309526e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.1999999999999225 y[1] (closed_form) = 10.24299055369869 y[1] (numeric) = 10.24299055369574 absolute error = 2.950528710243816e-12 relative error = 2.880534444287265e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.2999999999999114 y[1] (closed_form) = 10.26568495866571 y[1] (numeric) = 10.26568495866237 absolute error = 3.343103571751271e-12 relative error = 3.256581109991315e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.3999999999999004 y[1] (closed_form) = 10.28940692210277 y[1] (numeric) = 10.28940692209903 absolute error = 3.739231146937527e-12 relative error = 3.634058964958663e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.4999999999998894 y[1] (closed_form) = 10.31415900337371 y[1] (numeric) = 10.31415900336954 absolute error = 4.170885858911788e-12 relative error = 4.04384483266887e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.5999999999998784 y[1] (closed_form) = 10.33994389122063 y[1] (numeric) = 10.33994389121598 absolute error = 4.654054919228656e-12 relative error = 4.501044655745461e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.6999999999998674 y[1] (closed_form) = 10.36676440661376 y[1] (numeric) = 10.36676440660862 absolute error = 5.144329406903125e-12 relative error = 4.962328847389605e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.7999999999998564 y[1] (closed_form) = 10.39462350578328 y[1] (numeric) = 10.39462350577764 absolute error = 5.638156608256395e-12 relative error = 5.424108535647763e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 Finished! diff ( y , x , 1 ) = arcsin ( 0.1 * x + 0.2 ) ; Iterations = 16001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 6 Minutes 0.0 Seconds Percent Done = 100 %