##############ECHO OF PROBLEM################# ##############temp/expt_sin_cpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 0.2 * x + 0.3 ) , 2.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // 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; // 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(-2.5000000000000000000000000000000)*sin(c(0.20000000000000000000000000000000)*c(x)+c(0.30000000000000000000000000000000))*cos(c(0.20000000000000000000000000000000)*c(x)+c(0.30000000000000000000000000000000))+c(0.50000000000000000000000000000000)*c(x)+c(0.75000000000000000000000000000000)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.05350569829701002 y[1] (numeric) = 0.05350569829701002 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0.05450120214864118 y[1] (numeric) = 0.05450120202857519 absolute error = 1.200659918709768e-10 relative error = 2.202997129192136e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.05550871396502721 y[1] (numeric) = 0.05550871372505543 absolute error = 2.399717785595001e-10 relative error = 4.323137061159304e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.05652829762589406 y[1] (numeric) = 0.05652829726617736 absolute error = 3.597167078095431e-10 relative error = 6.363480290706061e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.05756001681781808 y[1] (numeric) = 0.05756001633851832 absolute error = 4.792997665425958e-10 relative error = 8.32695668000961e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.05860393503320782 y[1] (numeric) = 0.05860393443448743 absolute error = 5.987203927082518e-10 relative error = 1.021638551010249e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.05966011556928719 y[1] (numeric) = 0.0596601148513097 absolute error = 7.179774830223806e-10 relative error = 1.203446349661436e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.06072862152708347 y[1] (numeric) = 0.06072862069001327 absolute error = 8.370702048177137e-10 relative error = 1.378378405056339e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.0618095158104176 y[1] (numeric) = 0.06180951485441977 absolute error = 9.559978364492849e-10 relative error = 1.546683910907061e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.06290286112489729 y[1] (numeric) = 0.0629028600501379 absolute error = 1.07475939259416e-09 relative error = 1.708601760514777e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 Finished! diff ( y , x , 1 ) = expt ( sin ( 0.2 * x + 0.3 ) , 2.0 ) ; 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 %