##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos ( x ) ; diff ( y1 , x , 1 ) = m1 * y2 ; ! /* 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(5.0); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y2 (double x) { return(sin(c(x))); } double exact_soln_y2p (double x) { return( cos(c(x))); } double exact_soln_y2pp (double x) { return( glob__m1 * sin(c(x))); } double exact_soln_y1 (double x) { return( cos(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (closed_form) = 0.09983341664682815 y2[1] (numeric) = 0.09983341664682815 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 y1[1] (closed_form) = 0.9950041652780258 y1[1] (numeric) = 0.9950041652780258 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1993346653975308 y2[1] (closed_form) = 0.1980172146637207 y2[1] (numeric) = 0.1980172146637206 absolute error = 8.326672684688674e-17 relative error = 4.20502464840206e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 y1[1] (closed_form) = 0.9801985424886236 y1[1] (numeric) = 0.9801985424886235 absolute error = 1.110223024625157e-16 relative error = 1.132651168615711e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1941 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1941 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3086027973348146 y2[1] (closed_form) = 0.3037277361104648 y2[1] (numeric) = 0.3037277361104645 absolute error = 2.775557561562891e-16 relative error = 9.138307871077767e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 y1[1] (closed_form) = 0.952758868926032 y1[1] (numeric) = 0.952758868926032 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2894 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2894 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4079374627323454 y2[1] (closed_form) = 0.3967168855958872 y2[1] (numeric) = 0.3967168855958869 absolute error = 3.33066907387547e-16 relative error = 8.395581823729659e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 y1[1] (closed_form) = 0.9179410180850944 y1[1] (numeric) = 0.9179410180850947 absolute error = 2.220446049250313e-16 relative error = 2.418941964138784e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3642 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3642 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5072721281298761 y2[1] (closed_form) = 0.4857946983114446 y2[1] (numeric) = 0.4857946983114444 absolute error = 2.220446049250313e-16 relative error = 4.570749859906412e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 y1[1] (closed_form) = 0.8740729438053167 y1[1] (numeric) = 0.8740729438053172 absolute error = 4.440892098500626e-16 relative error = 5.080688207973809e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4246 Order of pole (three term test) = 32.76 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4246 Order of pole (three term test) = 32.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6066067935274063 y2[1] (closed_form) = 0.5700829325263109 y2[1] (numeric) = 0.5700829325263111 absolute error = 2.220446049250313e-16 relative error = 3.894952685937205e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.009933466539753067 y1[1] (closed_form) = 0.8215871530411133 y1[1] (numeric) = 0.8215871530411135 absolute error = 2.220446049250313e-16 relative error = 2.702629953537259e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4684 Order of pole (three term test) = 32.68 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4684 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7059414589249365 y2[1] (closed_form) = 0.6487505682317052 y2[1] (numeric) = 0.6487505682317058 absolute error = 6.661338147750939e-16 relative error = 1.02679496156862e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 y1[1] (closed_form) = 0.7610011170944755 y1[1] (numeric) = 0.7610011170944754 absolute error = 1.110223024625157e-16 relative error = 1.458898022205303e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4937 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4937 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8052761243224668 y2[1] (closed_form) = 0.7210220003870942 y2[1] (numeric) = 0.7210220003870953 absolute error = 1.110223024625157e-15 relative error = 1.539790774801757e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 y1[1] (closed_form) = 0.6929121697284535 y1[1] (numeric) = 0.6929121697284532 absolute error = 3.33066907387547e-16 relative error = 4.806769485923059e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4996 Order of pole (three term test) = 32.48 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4996 Order of pole (three term test) = 32.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.904610789719997 y2[1] (closed_form) = 0.7861846858155582 y2[1] (numeric) = 0.7861846858155596 absolute error = 1.332267629550188e-15 relative error = 1.69459880558236e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 y1[1] (closed_form) = 0.6179916178954954 y1[1] (numeric) = 0.6179916178954946 absolute error = 7.771561172376096e-16 relative error = 1.257551226801638e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4859 Order of pole (three term test) = 32.38 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4859 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.003945455117527 y2[1] (closed_form) = 0.8435961683555536 y2[1] (numeric) = 0.843596168355555 absolute error = 1.332267629550188e-15 relative error = 1.579271788475777e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 y1[1] (closed_form) = 0.536978123144536 y1[1] (numeric) = 0.5369781231445349 absolute error = 1.110223024625157e-15 relative error = 2.067538651525889e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.453 Order of pole (three term test) = 32.29 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.453 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.103280120515058 y2[1] (closed_form) = 0.8926904130062412 y2[1] (numeric) = 0.8926904130062426 absolute error = 1.443289932012704e-15 relative error = 1.616786638440815e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 y1[1] (closed_form) = 0.450670418961292 y1[1] (numeric) = 0.4506704189612903 absolute error = 1.665334536937735e-15 relative error = 3.695238175995683e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4023 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4023 Order of pole (three term test) = 32.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.202614785912588 y2[1] (closed_form) = 0.9329833866163663 y2[1] (numeric) = 0.9329833866163676 absolute error = 1.332267629550188e-15 relative error = 1.427965008446612e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 y1[1] (closed_form) = 0.3599194358434344 y1[1] (numeric) = 0.3599194358434322 absolute error = 2.220446049250313e-15 relative error = 6.169286312774204e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3358 Order of pole (three term test) = 32.13 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3358 Order of pole (three term test) = 32.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.301949451310118 y2[1] (closed_form) = 0.9640778300952001 y2[1] (numeric) = 0.9640778300952015 absolute error = 1.443289932012704e-15 relative error = 1.497067857965557e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 y1[1] (closed_form) = 0.265619911751605 y1[1] (numeric) = 0.2656199117516023 absolute error = 2.720046410331634e-15 relative error = 1.024037088332177e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2561 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2561 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.401284116707648 y2[1] (closed_form) = 0.9856671750950544 y2[1] (numeric) = 0.9856671750950556 absolute error = 1.221245327087672e-15 relative error = 1.239003750905978e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.009933466539753067 y1[1] (closed_form) = 0.1687015706510621 y1[1] (numeric) = 0.1687015706510588 absolute error = 3.275157922644212e-15 relative error = 1.941391482014392e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.009933466539753067 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1663 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1663 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.505055086899326 y2[1] (closed_form) = 0.9978398228643586 y2[1] (numeric) = 0.9978398228643596 absolute error = 9.992007221626409e-16 relative error = 1.001363845446031e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.007275776712777519 y1[1] (closed_form) = 0.06569389550046194 y1[1] (numeric) = 0.06569389550045832 absolute error = 3.622102617839573e-15 relative error = 5.513606082035588e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.007275776712777519 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06555 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06555 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.599998651048266 y2[1] (closed_form) = 0.999573642429342 y2[1] (numeric) = 0.9995736424293427 absolute error = 6.661338147750939e-16 relative error = 6.664179471120675e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001474401342213636 y1[1] (closed_form) = -0.02919817392471663 y1[1] (numeric) = -0.02919817392470994 absolute error = 6.689093723366568e-15 relative error = 2.290928789113132e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001474401342213636 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! Maximum Iterations Reached before Solution Completed! diff ( y2 , x , 3 ) = m1 * cos ( x ) ; diff ( y1 , x , 1 ) = m1 * y2 ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 32.46 %