##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.1; x_end = 0.5 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.05; glob_look_poles = true; glob_max_iter = 1000000; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt( 0.1 * x + 0.2))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.6560431130637943 y[1] (numeric) = 0.6560431130637943 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2000000000000001 y[1] (analytic) = 0.7042567802094299 y[1] (numeric) = 0.7042567802094304 absolute error = 4.440892098500626e-16 relative error = 6.305785365928612e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.7536775977668658 y[1] (numeric) = 0.7536775977668665 absolute error = 6.661338147750939e-16 relative error = 8.838445201885227e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.8042866614776244 y[1] (numeric) = 0.8042866614776252 absolute error = 7.771561172376096e-16 relative error = 9.662675690901413e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.8560665704653496 y[1] (numeric) = 0.8560665704653513 absolute error = 1.665334536937735e-15 relative error = 1.945332985065022e-13 % Correct digits = 14 h = 0.005 Finished! diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2)); Iterations = 80 Total Elapsed Time = 4 Seconds Elapsed Time(since restart) = 4 Seconds Time to Timeout = 9 Minutes 56 Seconds Percent Done = 101.3 %