##############ECHO OF PROBLEM################# ##############temp/mult_sin_sinpostode.ode################# diff ( y , x , 1 ) = sin(x) * sin(x); ! /* 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(-(sin(x) * cos(x))/2.0 + x/2.0); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.0003326673012346977 y[1] (numeric) = 0.0003326673012346977 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) = 0.002645414422837385 y[1] (numeric) = 0.002645414422908384 absolute error = 7.099876242477876e-14 relative error = 2.683842720893153e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.008839381651241179 y[1] (numeric) = 0.00883938165142786 absolute error = 1.866805321437681e-13 relative error = 2.111918452096199e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.02066097727511936 y[1] (numeric) = 0.02066097727546177 absolute error = 3.42410128029158e-13 relative error = 1.657279437800359e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.03963225379802596 y[1] (numeric) = 0.03963225379855796 absolute error = 5.320049956125672e-13 relative error = 1.342353625215899e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.06699022850819354 y[1] (numeric) = 0.06699022850894147 absolute error = 7.479294961143523e-13 relative error = 1.11647551108573e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.1036375675028852 y[1] (numeric) = 0.1036375675038667 absolute error = 9.815204204954853e-13 relative error = 9.470701060869272e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.1501065992396241 y[1] (numeric) = 0.1501065992408475 absolute error = 1.223465773136923e-12 relative error = 8.150646136375601e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.2065380922804516 y[1] (numeric) = 0.2065380922819158 absolute error = 1.464189880451272e-12 relative error = 7.08920017748152e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.2726756432935801 y[1] (numeric) = 0.2726756432952741 absolute error = 1.694033802124295e-12 relative error = 6.212633375179718e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.3518572334383119 y[1] (numeric) = 0.3518572334402274 absolute error = 1.915467784385783e-12 relative error = 5.443877807109527e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.435486101645874 y[1] (numeric) = 0.4354861016479711 absolute error = 2.097100271214458e-12 relative error = 4.815538919126668e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.5257732869379812 y[1] (numeric) = 0.5257732869402241 absolute error = 2.242872554347741e-12 relative error = 4.265854903754942e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.6211126663706023 y[1] (numeric) = 0.6211126663729494 absolute error = 2.347122496360043e-12 relative error = 3.778899744671403e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.719696701962444 y[1] (numeric) = 0.7196967019648496 absolute error = 2.405631249757789e-12 relative error = 3.342562558919886e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.8195885015302498 y[1] (numeric) = 0.8195885015326657 absolute error = 2.415956323886803e-12 relative error = 2.947767470353699e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.9187990364679293 y[1] (numeric) = 0.9187990364703074 absolute error = 2.378097718747085e-12 relative error = 2.588267536597588e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 1.01536643804034 y[1] (numeric) = 1.015366438042634 absolute error = 2.293498724270648e-12 relative error = 2.258789180285599e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 1.107434210898724 y[1] (numeric) = 1.107434210900889 absolute error = 2.165378987228905e-12 relative error = 1.955311625664535e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 1.193325245691752 y[1] (numeric) = 1.19332524569375 absolute error = 1.998845533535132e-12 relative error = 1.675021575845765e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 1.271608680122934 y[1] (numeric) = 1.271608680124734 absolute error = 1.800781745942004e-12 relative error = 1.41614458448641e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 1.341156942915038 y[1] (numeric) = 1.341156942916618 absolute error = 1.579625319436673e-12 relative error = 1.177807957362035e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 1.401190706518654 y[1] (numeric) = 1.401190706519997 absolute error = 1.343369859796439e-12 relative error = 9.587344917053624e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 1.451309956442278 y[1] (numeric) = 1.451309956443379 absolute error = 1.101785329638005e-12 relative error = 7.591661069692567e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 1.491509938567769 y[1] (numeric) = 1.491509938568633 absolute error = 8.648637361829969e-13 relative error = 5.798578432628398e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 1.522181348682039 y[1] (numeric) = 1.52218134868268 absolute error = 6.414868636284154e-13 relative error = 4.214260437390319e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 1.54409475666894 y[1] (numeric) = 1.544094756669381 absolute error = 4.409805853811122e-13 relative error = 2.855916604058906e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 1.558369886319667 y[1] (numeric) = 1.558369886319939 absolute error = 2.715605518233133e-13 relative error = 1.742593682072783e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 1.566430975478699 y[1] (numeric) = 1.566430975478839 absolute error = 1.398881011027697e-13 relative error = 8.930371225583056e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 1.569949996175378 y[1] (numeric) = 1.569949996175429 absolute error = 5.10702591327572e-14 relative error = 3.252986353525375e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 1.570779998375316 y[1] (numeric) = 1.570779998375324 absolute error = 8.43769498715119e-15 relative error = 5.371659300397535e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 1.570881234725899 y[1] (numeric) = 1.570881234725914 absolute error = 1.443289932012704e-14 relative error = 9.187772443309765e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 1.572243011469176 y[1] (numeric) = 1.572243011469244 absolute error = 6.794564910705958e-14 relative error = 4.321574248472444e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 1.576804381079604 y[1] (numeric) = 1.576804381079772 absolute error = 1.680877659282487e-13 relative error = 1.066002656671734e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 1.586376838360923 y[1] (numeric) = 1.586376838361232 absolute error = 3.095301792654936e-13 relative error = 1.95117686908053e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 1.60257210186484 y[1] (numeric) = 1.602572101865328 absolute error = 4.882760862301438e-13 relative error = 3.046827569642323e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 1.626737859758438 y[1] (numeric) = 1.626737859759134 absolute error = 6.963318810448982e-13 relative error = 4.28054143369049e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 1.659904041749834 y[1] (numeric) = 1.659904041750759 absolute error = 9.248157795127554e-13 relative error = 5.571501461842549e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 1.702741759040847 y[1] (numeric) = 1.702741759042012 absolute error = 1.165512131251489e-12 relative error = 6.84491423942067e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 1.755536549241193 y[1] (numeric) = 1.755536549242602 absolute error = 1.408873018249324e-12 relative error = 8.025312938419252e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 1.818176992885057 y[1] (numeric) = 1.818176992886702 absolute error = 1.645572567099407e-12 relative error = 9.050673138747822e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 1.890159155373582 y[1] (numeric) = 1.890159155375447 absolute error = 1.864952636765338e-12 relative error = 9.866643406526993e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 1.970606677257076 y[1] (numeric) = 1.970606677259136 absolute error = 2.05968575528459e-12 relative error = 1.045203885207323e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 2.058305711920758 y[1] (numeric) = 2.058305711922979 absolute error = 2.220890138460163e-12 relative error = 1.078989445347108e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 2.151753317818768 y[1] (numeric) = 2.151753317821111 absolute error = 2.34301467116893e-12 relative error = 1.088886282533559e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 2.249217376010801 y[1] (numeric) = 2.249217376013222 absolute error = 2.421174372102541e-12 relative error = 1.076451924089579e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 2.348805644278239 y[1] (numeric) = 2.348805644280691 absolute error = 2.451372438372346e-12 relative error = 1.043667637781765e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 2.448541194850089 y[1] (numeric) = 2.448541194852522 absolute error = 2.433164780768493e-12 relative error = 9.937201734183863e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 2.546441228274656 y[1] (numeric) = 2.546441228277023 absolute error = 2.366995488500834e-12 relative error = 9.295307750356343e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 2.6405961213766 y[1] (numeric) = 2.640596121378856 absolute error = 2.255973186038318e-12 relative error = 8.543423841970314e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = sin(x) * sin(x); Iterations = 981 Total Elapsed Time = 1 Minutes 17 Seconds Elapsed Time(since restart) = 1 Minutes 17 Seconds Time to Timeout = 8 Minutes 43 Seconds Percent Done = 100.2 %