##############ECHO OF PROBLEM################# ##############temp/div_sin_linpostode.ode################# diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3); ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.1; x_end = 5.0 ; 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(0.35368600833851455044094925717134 * Si(x + 1.5000000000000000000000000000000) - 4.9874749330202721547086168557074 * Ci(x + 1.5000000000000000000000000000000)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.2000000000000001 y[1] (analytic) = 0 y[1] (numeric) = 0.04512790218977705 absolute error = 0.04512790218977705 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 0.3000000000000002 y[1] (analytic) = 0 y[1] (numeric) = 0.1156726715788302 absolute error = 0.1156726715788302 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.4000000000000002 y[1] (analytic) = 0 y[1] (numeric) = 0.2082173190608125 absolute error = 0.2082173190608125 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.5000000000000003 y[1] (analytic) = 0 y[1] (numeric) = 0.3196262292174508 absolute error = 0.3196262292174508 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.6000000000000004 y[1] (analytic) = 0 y[1] (numeric) = 0.4469985422385146 absolute error = 0.4469985422385146 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 0.7000000000000005 y[1] (analytic) = 0 y[1] (numeric) = 0.5876345303263925 absolute error = 0.5876345303263925 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.8000000000000006 y[1] (analytic) = 0 y[1] (numeric) = 0.7390114023125733 absolute error = 0.7390114023125733 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.9000000000000007 y[1] (analytic) = 0 y[1] (numeric) = 0.8987660153928099 absolute error = 0.8987660153928099 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.000000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.064682677330267 absolute error = 1.064682677330267 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 1.104999999999998 y[1] (analytic) = 0 y[1] (numeric) = 1.243256633285376 absolute error = 1.243256633285376 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 1.283 Order of pole = 0.6214 Complex estimate of poles used Complex estimate of poles used x[1] = 1.204999999999996 y[1] (analytic) = 0 y[1] (numeric) = 1.415459111000753 absolute error = 1.415459111000753 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 1.304999999999994 y[1] (analytic) = 0 y[1] (numeric) = 1.587902617054081 absolute error = 1.587902617054081 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.404999999999992 y[1] (analytic) = 0 y[1] (numeric) = 1.758907267027318 absolute error = 1.758907267027318 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.50499999999999 y[1] (analytic) = 0 y[1] (numeric) = 1.926919353177417 absolute error = 1.926919353177417 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.604999999999988 y[1] (analytic) = 0 y[1] (numeric) = 2.090510776192209 absolute error = 2.090510776192209 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.704999999999986 y[1] (analytic) = 0 y[1] (numeric) = 2.248378828538296 absolute error = 2.248378828538296 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 1.804999999999984 y[1] (analytic) = 0 y[1] (numeric) = 2.399346112327569 absolute error = 2.399346112327569 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.904999999999981 y[1] (analytic) = 0 y[1] (numeric) = 2.542360418968709 absolute error = 2.542360418968709 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.004999999999979 y[1] (analytic) = 0 y[1] (numeric) = 2.676494433378251 absolute error = 2.676494433378251 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.104999999999977 y[1] (analytic) = 0 y[1] (numeric) = 2.800945154435226 absolute error = 2.800945154435226 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 2.204999999999975 y[1] (analytic) = 0 y[1] (numeric) = 2.915032947281919 absolute error = 2.915032947281919 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.304999999999973 y[1] (analytic) = 0 y[1] (numeric) = 3.018200163167139 absolute error = 3.018200163167139 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.404999999999971 y[1] (analytic) = 0 y[1] (numeric) = 3.110009279648683 absolute error = 3.110009279648683 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 2.504999999999969 y[1] (analytic) = 0 y[1] (numeric) = 3.190140528742591 absolute error = 3.190140528742591 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.604999999999967 y[1] (analytic) = 0 y[1] (numeric) = 3.258388993487435 absolute error = 3.258388993487435 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.704999999999965 y[1] (analytic) = 0 y[1] (numeric) = 3.314661164720956 absolute error = 3.314661164720956 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.804999999999962 y[1] (analytic) = 0 y[1] (numeric) = 3.358970959893804 absolute error = 3.358970959893804 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.90499999999996 y[1] (analytic) = 0 y[1] (numeric) = 3.391435214655313 absolute error = 3.391435214655313 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 3.004999999999958 y[1] (analytic) = 0 y[1] (numeric) = 3.412268665875084 absolute error = 3.412268665875084 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 5.23 Order of pole = 1.174 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.104999999999956 y[1] (analytic) = 0 y[1] (numeric) = 3.421778451811681 absolute error = 3.421778451811681 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.9 Order of pole = 0.6982 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.204999999999954 y[1] (analytic) = 0 y[1] (numeric) = 3.420358161379432 absolute error = 3.420358161379432 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 0 y[1] (numeric) = 3.408481469950295 absolute error = 3.408481469950295 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 9.595 Order of pole = 2.494 Complex estimate of poles used x[1] = 3.40499999999995 y[1] (analytic) = 0 y[1] (numeric) = 3.386695403900001 absolute error = 3.386695403900001 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 6.205 Order of pole = 1.3 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.504999999999947 y[1] (analytic) = 0 y[1] (numeric) = 3.355613280196394 absolute error = 3.355613280196394 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.604999999999945 y[1] (analytic) = 0 y[1] (numeric) = 3.315907370756205 absolute error = 3.315907370756205 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.704999999999943 y[1] (analytic) = 0 y[1] (numeric) = 3.26830134408346 absolute error = 3.26830134408346 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.804999999999941 y[1] (analytic) = 0 y[1] (numeric) = 3.213562538864578 absolute error = 3.213562538864578 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 3.904999999999939 y[1] (analytic) = 0 y[1] (numeric) = 3.152494125747335 absolute error = 3.152494125747335 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.004999999999937 y[1] (analytic) = 0 y[1] (numeric) = 3.085927214488461 absolute error = 3.085927214488461 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 0 y[1] (numeric) = 3.014712964033904 absolute error = 3.014712964033904 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.204999999999933 y[1] (analytic) = 0 y[1] (numeric) = 2.939714752914265 absolute error = 2.939714752914265 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.30499999999993 y[1] (analytic) = 0 y[1] (numeric) = 2.861800466615194 absolute error = 2.861800466615194 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.404999999999928 y[1] (analytic) = 0 y[1] (numeric) = 2.781834957340336 absolute error = 2.781834957340336 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.504999999999926 y[1] (analytic) = 0 y[1] (numeric) = 2.700672729846834 absolute error = 2.700672729846834 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.604999999999924 y[1] (analytic) = 0 y[1] (numeric) = 2.619150904827284 absolute error = 2.619150904827284 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.704999999999922 y[1] (analytic) = 0 y[1] (numeric) = 2.538082508666498 absolute error = 2.538082508666498 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 4.80499999999992 y[1] (analytic) = 0 y[1] (numeric) = 2.458250135348046 absolute error = 2.458250135348046 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.904999999999918 y[1] (analytic) = 0 y[1] (numeric) = 2.380400022858657 absolute error = 2.380400022858657 relative error = -1 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 4.602 Order of pole = 0.7581 Complex estimate of poles used Complex estimate of poles used x[1] = 5.004999999999916 y[1] (analytic) = 0 y[1] (numeric) = 2.305236582674028 absolute error = 2.305236582674028 relative error = -1 % Correct digits = -1 h = 0.005 Finished! diff ( y , x , 1 ) = sin(x) / (0.2 * x + 0.3); Iterations = 981 Total Elapsed Time = 32 Seconds Elapsed Time(since restart) = 31 Seconds Time to Timeout = 9 Minutes 28 Seconds Percent Done = 100.2 %