##############ECHO OF PROBLEM################# ##############temp/expt_sin_cpostode.ode################# diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0); ! // 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(-2.5000000000000000000000000000000*sin(.20000000000000000000000000000000*x+.30000000000000000000000000000000)*cos(.20000000000000000000000000000000*x+.30000000000000000000000000000000)+.50000000000000000000000000000000*x+.75000000000000000000000000000000); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.05350569829700989 y[1] (numeric) = 0.05350569829700989 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) = 0.0640087199769144 y[1] (numeric) = 0.06400871997691435 absolute error = 5.551115123125783e-17 relative error = 8.672435763639496e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.07576916003565855 y[1] (numeric) = 0.07576916003565863 absolute error = 8.326672684688674e-17 relative error = 1.098952750798606e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.08884819361181087 y[1] (numeric) = 0.08884819361181095 absolute error = 8.326672684688674e-17 relative error = 9.371797384051467e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.1033048863755965 y[1] (numeric) = 0.1033048863755967 absolute error = 1.804112415015879e-16 relative error = 1.74639601117848e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.119196100036426 y[1] (numeric) = 0.1191961000364261 absolute error = 1.249000902703301e-16 relative error = 1.047853832735811e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.1365764013762884 y[1] (numeric) = 0.1365764013762886 absolute error = 2.220446049250313e-16 relative error = 1.625790419775853e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.1554979749545426 y[1] (numeric) = 0.1554979749545427 absolute error = 1.387778780781446e-16 relative error = 8.924738609535854e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.1760105396237524 y[1] (numeric) = 0.1760105396237526 absolute error = 1.942890293094024e-16 relative error = 1.103848836124944e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.1981612689901296 y[1] (numeric) = 0.1981612689901298 absolute error = 2.220446049250313e-16 relative error = 1.120524742582726e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.2232313221562945 y[1] (numeric) = 0.2232313221562952 absolute error = 7.216449660063518e-16 relative error = 3.232722715771468e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.2488766261627098 y[1] (numeric) = 0.2488766261627111 absolute error = 1.360023205165817e-15 relative error = 5.464648191898364e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.276287492140168 y[1] (numeric) = 0.27628749214017 absolute error = 1.998401444325282e-15 relative error = 7.233050721353102e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.3055000578843469 y[1] (numeric) = 0.3055000578843496 absolute error = 2.775557561562891e-15 relative error = 9.085293079105189e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.3365475788556399 y[1] (numeric) = 0.3365475788556433 absolute error = 3.441691376337985e-15 relative error = 1.022646303990877e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.3694603749775127 y[1] (numeric) = 0.369460374977517 absolute error = 4.274358644806853e-15 relative error = 1.156919370600166e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.4042657821310947 y[1] (numeric) = 0.4042657821310999 absolute error = 5.218048215738236e-15 relative error = 1.29074694084451e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.4409881084236 y[1] (numeric) = 0.440988108423606 absolute error = 5.995204332975845e-15 relative error = 1.359493423622442e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.4796485953005411 y[1] (numeric) = 0.4796485953005479 absolute error = 6.827871601444713e-15 relative error = 1.423515396134219e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.5202653835639478 y[1] (numeric) = 0.5202653835639557 absolute error = 7.882583474838611e-15 relative error = 1.515108197443571e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.5628534843509538 y[1] (numeric) = 0.5628534843509624 absolute error = 8.548717289613705e-15 relative error = 1.518817512424487e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.6074247551191786 y[1] (numeric) = 0.6074247551191881 absolute error = 9.547918011776346e-15 relative error = 1.571868438240225e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.6539878806773263 y[1] (numeric) = 0.6539878806773372 absolute error = 1.088018564132653e-14 relative error = 1.663667777766474e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.702548359291343 y[1] (numeric) = 0.7025483592913547 absolute error = 1.176836406102666e-14 relative error = 1.675096654256989e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.7531084938883644 y[1] (numeric) = 0.7531084938883773 absolute error = 1.287858708565182e-14 relative error = 1.71005734102912e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.8056673883725248 y[1] (numeric) = 0.8056673883725388 absolute error = 1.398881011027697e-14 relative error = 1.736300899374224e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.8602209490585176 y[1] (numeric) = 0.860220949058533 absolute error = 1.532107773982716e-14 relative error = 1.781063081129976e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.9167618912206199 y[1] (numeric) = 0.9167618912206366 absolute error = 1.665334536937735e-14 relative error = 1.816539881168522e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.9752797507466986 y[1] (numeric) = 0.9752797507467167 absolute error = 1.809663530139005e-14 relative error = 1.855532762526323e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 1.035760900878559 y[1] (numeric) = 1.035760900878578 absolute error = 1.953992523340276e-14 relative error = 1.886528562415176e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 1.098188574011848 y[1] (numeric) = 1.09818857401187 absolute error = 2.109423746787797e-14 relative error = 1.920821065440296e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 3.204999999999954 y[1] (analytic) = 1.16254288852065 y[1] (numeric) = 1.162542888520673 absolute error = 2.242650509742816e-14 relative error = 1.929090558195763e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 1.228800880563841 y[1] (numeric) = 1.228800880563865 absolute error = 2.398081733190338e-14 relative error = 1.951562511975063e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 1.296936540822337 y[1] (numeric) = 1.296936540822362 absolute error = 2.509104035652854e-14 relative error = 1.934639017929072e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 1.36692085610846 y[1] (numeric) = 1.366920856108487 absolute error = 2.708944180085382e-14 relative error = 1.981785681284855e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 53.87 Order of pole = 0.06594 x[1] = 3.604999999999945 y[1] (analytic) = 1.438721855780845 y[1] (numeric) = 1.438721855780874 absolute error = 2.886579864025407e-14 relative error = 2.00635018674875e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used x[1] = 3.704999999999943 y[1] (analytic) = 1.512304662890649 y[1] (numeric) = 1.512304662890679 absolute error = 3.019806626980426e-14 relative error = 1.996824251806714e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 3.804999999999941 y[1] (analytic) = 1.587631549977226 y[1] (numeric) = 1.587631549977258 absolute error = 3.175237850427948e-14 relative error = 1.999984096104348e-12 % Correct digits = 13 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] = 3.904999999999939 y[1] (analytic) = 1.664661999424019 y[1] (numeric) = 1.664661999424052 absolute error = 3.26405569239796e-14 relative error = 1.960791856561476e-12 % Correct digits = 13 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) = 1.743352768278101 y[1] (numeric) = 1.743352768278136 absolute error = 3.463895836830488e-14 relative error = 1.986916188082666e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.104999999999935 y[1] (analytic) = 1.823657957429677 y[1] (numeric) = 1.823657957429713 absolute error = 3.641531520770513e-14 relative error = 1.996828136512511e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 4.204999999999933 y[1] (analytic) = 1.905529085040866 y[1] (numeric) = 1.905529085040904 absolute error = 3.796962744218035e-14 relative error = 1.992602880756662e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.30499999999993 y[1] (analytic) = 1.988915164106302 y[1] (numeric) = 1.988915164106342 absolute error = 3.97459842815806e-14 relative error = 1.998375043786246e-12 % Correct digits = 13 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] = 4.404999999999928 y[1] (analytic) = 2.073762784021464 y[1] (numeric) = 2.073762784021506 absolute error = 4.218847493575595e-14 relative error = 2.034392518798297e-12 % Correct digits = 13 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] = 4.504999999999926 y[1] (analytic) = 2.160016196028249 y[1] (numeric) = 2.160016196028293 absolute error = 4.39648317751562e-14 relative error = 2.035393616769956e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 2.247617402401097 y[1] (numeric) = 2.247617402401142 absolute error = 4.485301019485632e-14 relative error = 1.995580304145203e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 2.336506249230972 y[1] (numeric) = 2.33650624923102 absolute error = 4.75175454539567e-14 relative error = 2.033700764532362e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 2.426620522658793 y[1] (numeric) = 2.426620522658843 absolute error = 4.973799150320701e-14 relative error = 2.049681482488668e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 2.51789604840433 y[1] (numeric) = 2.517896048404382 absolute error = 5.195843755245733e-14 relative error = 2.063565633910304e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 2.610266794431366 y[1] (numeric) = 2.610266794431421 absolute error = 5.551115123125783e-14 relative error = 2.126646645840303e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = expt(sin(0.2 * x + 0.3) , 2.0); Iterations = 981 Total Elapsed Time = 1 Minutes 26 Seconds Elapsed Time(since restart) = 1 Minutes 25 Seconds Time to Timeout = 8 Minutes 34 Seconds Percent Done = 100.2 %