##############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(0.1); x_end=c(0.2); 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=(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(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] = 0.1 y[1] (closed_form) = 10.22132127453915 y[1] (numeric) = 10.22132127453915 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] = 0.11 y[1] (closed_form) = 10.22344213854765 y[1] (numeric) = 10.2234421385439 absolute error = 3.749889287973929e-12 relative error = 3.667932225913338e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 10.22557323288207 y[1] (numeric) = 10.22557323287454 absolute error = 7.529976642217662e-12 relative error = 7.363867502316387e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 10.22771455980771 y[1] (numeric) = 10.22771455979639 absolute error = 1.13224984943372e-11 relative error = 1.107040915947313e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 10.22986612160207 y[1] (numeric) = 10.22986612158694 absolute error = 1.513811298536893e-11 relative error = 1.479795806262047e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 10.23202792055493 y[1] (numeric) = 10.23202792053595 absolute error = 1.897504375847348e-11 relative error = 1.854475369477332e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 10.2341999589683 y[1] (numeric) = 10.23419995894548 absolute error = 2.282618538629322e-11 relative error = 2.230382978426219e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 10.23638223915654 y[1] (numeric) = 10.23638223912984 absolute error = 2.670397236670397e-11 relative error = 2.608731458322752e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 10.2385747634463 y[1] (numeric) = 10.2385747634157 absolute error = 3.060129927234811e-11 relative error = 2.98882412634234e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 10.24077753417656 y[1] (numeric) = 10.24077753414205 absolute error = 3.451638974638627e-11 relative error = 3.370485261611696e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.001 Finished! diff ( y , x , 1 ) = arcsin ( 0.1 * x + 0.2 ) ; Iterations = 100 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 101 %