##############ECHO OF PROBLEM################# ##############temp/sub_sin_cospostode.ode################# diff ( y , x , 1 ) = m1 * 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 = 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(cos(x) - sin(x)) ; } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.8951707486311976 y[1] (numeric) = 0.8951707486311976 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) = 0.7813972470461803 y[1] (numeric) = 0.7813972470461675 absolute error = 1.27675647831893e-14 relative error = 1.633940333351948e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.6598162824642663 y[1] (numeric) = 0.6598162824642425 absolute error = 2.375877272697835e-14 relative error = 3.600816372436983e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.5316426516942343 y[1] (numeric) = 0.5316426516942014 absolute error = 3.286260152890463e-14 relative error = 6.181332785128954e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.3981570232861693 y[1] (numeric) = 0.3981570232861295 absolute error = 3.980149543281186e-14 relative error = 9.996431835940553e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.2606931415146424 y[1] (numeric) = 0.2606931415145977 absolute error = 4.474198789239381e-14 relative error = 1.716270233748393e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.1206245000467966 y[1] (numeric) = 0.1206245000467491 absolute error = 4.750366766614889e-14 relative error = 3.938144211807693e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = -0.02064938155235824 y[1] (numeric) = -0.0206493815524064 absolute error = 4.816633203397203e-14 relative error = 2.332579884382603e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -0.1617169413568199 y[1] (numeric) = -0.1617169413568667 absolute error = 4.679590048795035e-14 relative error = 2.89369190978561e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -0.3011686789397577 y[1] (numeric) = -0.301168678939801 absolute error = 4.329869796038111e-14 relative error = 1.437689274754965e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -0.4443297578974999 y[1] (numeric) = -0.4443297578975404 absolute error = 4.046762924758696e-14 relative error = 9.10756674031322e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = -0.5761461677243921 y[1] (numeric) = -0.5761461677244278 absolute error = 3.574918139293004e-14 relative error = 6.204880531294479e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -0.7022059154919849 y[1] (numeric) = -0.7022059154920136 absolute error = 2.875477633779155e-14 relative error = 4.094920834958385e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = -0.8212494538703967 y[1] (numeric) = -0.8212494538704168 absolute error = 2.009503674571533e-14 relative error = 2.446885858007107e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -0.9320873391747128 y[1] (numeric) = -0.9320873391747221 absolute error = 9.325873406851315e-15 relative error = 1.000536432037433e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -1.033612115893106 y[1] (numeric) = -1.033612115893103 absolute error = 3.33066907387547e-15 relative error = 3.222358777206827e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -1.124809382016235 y[1] (numeric) = -1.124809382016218 absolute error = 1.731947918415244e-14 relative error = 1.539770156709313e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = -1.204767924606807 y[1] (numeric) = -1.204767924606774 absolute error = 3.286260152890463e-14 relative error = 2.727712189020122e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = -1.272688824338037 y[1] (numeric) = -1.272688824337986 absolute error = 5.062616992290714e-14 relative error = 3.977890663826589e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = -1.327893438031474 y[1] (numeric) = -1.327893438031404 absolute error = 6.94999613415348e-14 relative error = 5.233850800901956e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = -1.369830179435312 y[1] (numeric) = -1.369830179435223 absolute error = 8.881784197001252e-14 relative error = 6.483857875479579e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = -1.398080030491889 y[1] (numeric) = -1.398080030491779 absolute error = 1.099120794378905e-13 relative error = 7.86164432941796e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = -1.412360728027606 y[1] (numeric) = -1.412360728027475 absolute error = 1.312283615106935e-13 relative error = 9.291419600285606e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = -1.412529584033258 y[1] (numeric) = -1.412529584033106 absolute error = 1.523225989785715e-13 relative error = 1.07836749545194e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = -1.398584911355452 y[1] (numeric) = -1.398584911355277 absolute error = 1.745270594710746e-13 relative error = 1.247883185740436e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = -1.370666040554088 y[1] (numeric) = -1.370666040553892 absolute error = 1.962874307537277e-13 relative error = 1.432058757904143e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -1.329051927757464 y[1] (numeric) = -1.329051927757245 absolute error = 2.182698466413058e-13 relative error = 1.642297355601425e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = -1.274158367424844 y[1] (numeric) = -1.274158367424605 absolute error = 2.395861287141088e-13 relative error = 1.880348117152248e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -1.206533837865675 y[1] (numeric) = -1.206533837865415 absolute error = 2.602362769721367e-13 relative error = 2.156891657779672e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -1.126854021025615 y[1] (numeric) = -1.126854021025335 absolute error = 2.793321129956894e-13 relative error = 2.478866896543114e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -1.035915051295882 y[1] (numeric) = -1.035915051295584 absolute error = 2.98205904414317e-13 relative error = 2.878671412692335e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -0.9346255608015913 y[1] (numeric) = -0.9346255608012756 absolute error = 3.157474282033945e-13 relative error = 3.378330760958329e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -0.823997600649906 y[1] (numeric) = -0.8239976006495744 absolute error = 3.316236174555343e-13 relative error = 4.024570183141007e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -0.7051365288499205 y[1] (numeric) = -0.7051365288495749 absolute error = 3.456124275658112e-13 relative error = 4.901354750824014e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = -0.5792299659408137 y[1] (numeric) = -0.5792299659404558 absolute error = 3.57824880836688e-13 relative error = 6.177596151391982e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = -0.4475359286799971 y[1] (numeric) = -0.4475359286796287 absolute error = 3.683719995706269e-13 relative error = 8.231115670581725e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = -0.3113702603555196 y[1] (numeric) = -0.3113702603551425 absolute error = 3.770872503139344e-13 relative error = 1.211057375496876e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -0.1720934833148937 y[1] (numeric) = -0.1720934833145099 absolute error = 3.838040996129166e-13 relative error = 2.230207049215445e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = -0.03109720507552771 y[1] (numeric) = -0.03109720507513941 absolute error = 3.883005028626485e-13 relative error = 1.248666887971311e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 0.1102097861575835 y[1] (numeric) = 0.1102097861579743 absolute error = 3.907846268802473e-13 relative error = 3.54582510777658e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 0.2504155976379199 y[1] (numeric) = 0.2504155976383111 absolute error = 3.911315715754426e-13 relative error = 1.561929749044571e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 0.3881193392430496 y[1] (numeric) = 0.3881193392434388 absolute error = 3.891886812823486e-13 relative error = 1.002755188755563e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 0.5219451207056592 y[1] (numeric) = 0.5219451207060444 absolute error = 3.851363672424668e-13 relative error = 7.378867087056398e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 0.6505557990542963 y[1] (numeric) = 0.6505557990546752 absolute error = 3.789191183045659e-13 relative error = 5.824544471902261e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 0.7726663389039394 y[1] (numeric) = 0.77266633890431 absolute error = 3.705924456198773e-13 relative error = 4.796280450699828e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 0.8870566521047888 y[1] (numeric) = 0.8870566521051492 absolute error = 3.603783937933258e-13 relative error = 4.062631095074117e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 0.9925837884597519 y[1] (numeric) = 0.9925837884601002 absolute error = 3.482769628249116e-13 relative error = 3.508791568773781e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 1.088193355705003 y[1] (numeric) = 1.088193355705338 absolute error = 3.346212196220222e-13 relative error = 3.075016198800741e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 1.17293005464895 y[1] (numeric) = 1.17293005464927 absolute error = 3.197442310920451e-13 relative error = 2.726029824410479e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 1.245947224205973 y[1] (numeric) = 1.245947224206275 absolute error = 3.024247519078926e-13 relative error = 2.427267752858668e-11 % Correct digits = 12 h = 0.005 Finished! diff ( y , x , 1 ) = m1 * sin(x) - cos(x); Iterations = 981 Total Elapsed Time = 33 Seconds Elapsed Time(since restart) = 33 Seconds Time to Timeout = 9 Minutes 27 Seconds Percent Done = 100.2 %