##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.1; x_end = 1.0 ; 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(2.0 - ln(fabs(cos(x)))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 2.005008355623235 y[1] (numeric) = 2.005008355623235 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE 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] = 0.2000000000000001 y[1] (analytic) = 2.020134773052408 y[1] (numeric) = 2.020134773052703 absolute error = 2.944311461305915e-13 relative error = 1.45748268906687e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.604 Order of pole = 6.724 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] = 0.3000000000000002 y[1] (analytic) = 2.045691655926058 y[1] (numeric) = 2.045691655926748 absolute error = 6.901146321069973e-13 relative error = 3.373502698257775e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.279 Order of pole = 2.218 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] = 0.4000000000000002 y[1] (analytic) = 2.082229019075056 y[1] (numeric) = 2.082229019076336 absolute error = 1.280309191997731e-12 relative error = 6.148743391187849e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.173 Order of pole = 2.086 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] = 0.5000000000000003 y[1] (analytic) = 2.130584240443723 y[1] (numeric) = 2.130584240445956 absolute error = 2.233324636335965e-12 relative error = 1.048221700856496e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.072 Order of pole = 2.082 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] = 0.6000000000000004 y[1] (analytic) = 2.191965169419438 y[1] (numeric) = 2.191965169423316 absolute error = 3.878231069620597e-12 relative error = 1.769294112756264e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9723 Order of pole = 2.082 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] = 0.7000000000000005 y[1] (analytic) = 2.268085757567932 y[1] (numeric) = 2.268085757574848 absolute error = 6.916689443414725e-12 relative error = 3.049571393116763e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8721 Order of pole = 2.082 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] = 0.8000000000000006 y[1] (analytic) = 2.361390746811344 y[1] (numeric) = 2.361390746824323 absolute error = 1.297895124707793e-11 relative error = 5.496316636543016e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.772 Order of pole = 2.082 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] = 0.9000000000000007 y[1] (analytic) = 2.475442443585815 y[1] (numeric) = 2.475442443612076 absolute error = 2.62607713352736e-11 relative error = 1.060851622840942e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6718 Order of pole = 2.082 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] = 1.000000000000001 y[1] (analytic) = 2.615626470386015 y[1] (numeric) = 2.615626470445116 absolute error = 5.910028022526603e-11 relative error = 2.259507651203117e-09 % Correct digits = 10 h = 0.005 Finished! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations = 180 Total Elapsed Time = 16 Seconds Elapsed Time(since restart) = 15 Seconds Time to Timeout = 9 Minutes 44 Seconds Percent Done = 100.6 %