##############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 = -0.8; x_end = 0.8 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 100; /* 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(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 - expt((0.1 * x + 0.2) , 2 ))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = -0.8 y[1] (analytic) = 10.07208677566643 y[1] (numeric) = 10.07208677566643 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 12.26 Order of pole = 10.62 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = -0.7 y[1] (analytic) = 10.08461961211218 y[1] (numeric) = 10.08461961211218 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 10.49 Order of pole = 5.766 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = -0.5999999999999999 y[1] (analytic) = 10.09816101618305 y[1] (numeric) = 10.09816101618305 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 9.583 Order of pole = 3.394 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = -0.4999999999999998 y[1] (analytic) = 10.11271237580762 y[1] (numeric) = 10.11271237580762 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 9.054 Order of pole = 2.117 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = -0.3999999999999997 y[1] (analytic) = 10.12827518812551 y[1] (numeric) = 10.12827518812551 absolute error = 1.77635683940025e-15 relative error = 1.753859177802425e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.713 Order of pole = 1.393 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = -0.2999999999999996 y[1] (analytic) = 10.14485106091358 y[1] (numeric) = 10.14485106091358 absolute error = 3.552713678800501e-15 relative error = 3.501987025209777e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.474 Order of pole = 0.9702 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = -0.1999999999999995 y[1] (analytic) = 10.16244171413014 y[1] (numeric) = 10.16244171413013 absolute error = 3.552713678800501e-15 relative error = 3.495925269476046e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.293 Order of pole = 0.7198 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = -0.09999999999999942 y[1] (analytic) = 10.18104898158116 y[1] (numeric) = 10.18104898158115 absolute error = 3.552713678800501e-15 relative error = 3.48953598516992e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.145 Order of pole = 0.5701 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 5.984795992119984e-16 y[1] (analytic) = 10.20067481271337 y[1] (numeric) = 10.20067481271337 absolute error = 3.552713678800501e-15 relative error = 3.48282220934311e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.017 Order of pole = 0.4802 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 0.1000000000000006 y[1] (analytic) = 10.22132127453915 y[1] (numeric) = 10.22132127453914 absolute error = 7.105427357601002e-15 relative error = 6.951574230721327e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.901 Order of pole = 0.426 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 0.2000000000000007 y[1] (analytic) = 10.24299055369871 y[1] (numeric) = 10.2429905536987 absolute error = 5.329070518200751e-15 relative error = 5.202651013161818e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.791 Order of pole = 0.3934 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 0.3000000000000008 y[1] (analytic) = 10.26568495866573 y[1] (numeric) = 10.26568495866572 absolute error = 8.881784197001252e-15 relative error = 8.651915807628342e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.685 Order of pole = 0.3737 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 0.4000000000000009 y[1] (analytic) = 10.28940692210279 y[1] (numeric) = 10.28940692210278 absolute error = 8.881784197001252e-15 relative error = 8.631969037906541e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.582 Order of pole = 0.3618 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 0.5000000000000009 y[1] (analytic) = 10.31415900337374 y[1] (numeric) = 10.31415900337373 absolute error = 1.243449787580175e-14 relative error = 1.205575546366355e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.48 Order of pole = 0.3547 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 0.600000000000001 y[1] (analytic) = 10.33994389122067 y[1] (numeric) = 10.33994389122066 absolute error = 8.881784197001252e-15 relative error = 8.589779877376806e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.379 Order of pole = 0.3503 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 0.7000000000000011 y[1] (analytic) = 10.3667644066138 y[1] (numeric) = 10.36676440661379 absolute error = 1.06581410364015e-14 relative error = 1.028106805398395e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.279 Order of pole = 0.3477 Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used Real estimate of pole used x[1] = 0.8000000000000012 y[1] (analytic) = 10.39462350578332 y[1] (numeric) = 10.39462350578331 absolute error = 1.06581410364015e-14 relative error = 1.025351329990121e-13 % Correct digits = 14 h = 0.005 Finished! diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ; Iterations = 320 Total Elapsed Time Unknown Elapsed Time(since restart) Unknown Time to Timeout = 26 Minutes 15 Seconds Percent Done = 100.3 %