##############ECHO OF PROBLEM################# ##############temp/sub_sin_cpostode.ode################# diff ( y , x , 1 ) = sin(x) - 1,0; ! /* 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(2.0 - cos(x) - x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.9049958347219742 y[1] (numeric) = 0.9049958347219742 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) = 0.8199334221587583 y[1] (numeric) = 0.8199334221587733 absolute error = 1.498801083243961e-14 relative error = 1.827954615263577e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 0.7446635108743939 y[1] (numeric) = 0.7446635108744235 absolute error = 2.964295475749168e-14 relative error = 3.980718045749888e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 0.6789390059971148 y[1] (numeric) = 0.6789390059971588 absolute error = 4.407585407761871e-14 relative error = 6.491872419804088e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 0.6224174381096271 y[1] (numeric) = 0.6224174381096851 absolute error = 5.795364188543317e-14 relative error = 9.311056910848588e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 0.5746643850903215 y[1] (numeric) = 0.5746643850903924 absolute error = 7.09432512735475e-14 relative error = 1.234516234417366e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 0.5351578127155114 y[1] (numeric) = 0.5351578127155943 absolute error = 8.282263763703668e-14 relative error = 1.547630169440598e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 0.5032932906528345 y[1] (numeric) = 0.5032932906529284 absolute error = 9.392486788328824e-14 relative error = 1.866205443777244e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 0.4783900317293354 y[1] (numeric) = 0.4783900317294394 absolute error = 1.040278974073772e-13 relative error = 2.174541493503241e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 0.4596976941318602 y[1] (numeric) = 0.4596976941319731 absolute error = 1.129651927556097e-13 relative error = 2.457380017294727e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 0.4458655667476386 y[1] (numeric) = 0.4458655667477592 absolute error = 1.20570220474292e-13 relative error = 2.704183266579434e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 0.4373069509982007 y[1] (numeric) = 0.4373069509983273 absolute error = 1.266209359584991e-13 relative error = 2.895470462325674e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 0.4323222859567867 y[1] (numeric) = 0.4323222859569178 absolute error = 1.31117339208231e-13 relative error = 3.032860980507884e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 0.4299622098043844 y[1] (numeric) = 0.4299622098045188 absolute error = 1.343924971308752e-13 relative error = 3.12568160797244e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 0.4292511366973765 y[1] (numeric) = 0.4292511366975126 absolute error = 1.360578316678129e-13 relative error = 3.169655710515547e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 0.4291970044988039 y[1] (numeric) = 0.4291970044989402 absolute error = 1.36279876272738e-13 relative error = 3.175228970478934e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 0.4288011871353061 y[1] (numeric) = 0.4288011871354411 absolute error = 1.35003119794419e-13 relative error = 3.148384935599991e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 0.4270684725387446 y[1] (numeric) = 0.4270684725388769 absolute error = 1.322830733840874e-13 relative error = 3.097467546543989e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 0.4230170064762142 y[1] (numeric) = 0.4230170064763422 absolute error = 1.279532035880493e-13 relative error = 3.024776820532958e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 0.4156881029129803 y[1] (numeric) = 0.4156881029131025 absolute error = 1.221800438599985e-13 relative error = 2.939223975952362e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 0.4041558228864385 y[1] (numeric) = 0.4041558228865533 absolute error = 1.147970607462412e-13 relative error = 2.840415855606697e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 0.3875362261821543 y[1] (numeric) = 0.3875362261822605 absolute error = 1.062483434566275e-13 relative error = 2.741636427214611e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 0.3649962033722938 y[1] (numeric) = 0.3649962033723899 absolute error = 9.60898027813073e-14 relative error = 2.632624720298701e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 0.3357617999696375 y[1] (numeric) = 0.3357617999697223 absolute error = 8.482103908136196e-14 relative error = 2.526226601389206e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 0.2991259495249808 y[1] (numeric) = 0.2991259495250531 absolute error = 7.227551890309769e-14 relative error = 2.416223634822487e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 0.25445553840137 y[1] (numeric) = 0.2544555384014286 absolute error = 5.861977570020827e-14 relative error = 2.303733535080038e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 0.2011977316362827 y[1] (numeric) = 0.2011977316363267 absolute error = 4.399258735077183e-14 relative error = 2.186534957078934e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 0.1388854966858304 y[1] (numeric) = 0.1388854966858591 absolute error = 2.867150961094467e-14 relative error = 2.064399112587098e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 0.06714226985955703 y[1] (numeric) = 0.06714226985956959 absolute error = 1.255939796607208e-14 relative error = 1.870564994651336e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -0.01431428117964202 y[1] (numeric) = -0.01431428117964612 absolute error = 4.102621020685149e-15 relative error = 2.866103417417814e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -0.1056694364441337 y[1] (numeric) = -0.1056694364441549 absolute error = 2.117750419472486e-14 relative error = 2.004127674696285e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -0.2070095723649095 y[1] (numeric) = -0.207009572364948 absolute error = 3.852473895449293e-14 relative error = 1.861012440844176e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -0.318321298746839 y[1] (numeric) = -0.318321298746895 absolute error = 5.601075159233915e-14 relative error = 1.759566570406729e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -0.4394915925590736 y[1] (numeric) = -0.4394915925591469 absolute error = 7.338574192772285e-14 relative error = 1.669787162489549e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = -0.5703089272238101 y[1] (numeric) = -0.5703089272239006 absolute error = 9.048317650695026e-14 relative error = 1.586564266973877e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = -0.7104653861199349 y[1] (numeric) = -0.7104653861200424 absolute error = 1.074695887837152e-13 relative error = 1.512664668586303e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = -0.8595597391841185 y[1] (numeric) = -0.8595597391842427 absolute error = 1.241229341530925e-13 relative error = 1.444029175574326e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -1.017101451868979 y[1] (numeric) = -1.017101451869119 absolute error = 1.396660564978447e-13 relative error = 1.373177240492585e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = -1.182515586402131 y[1] (numeric) = -1.182515586402286 absolute error = 1.549871342376719e-13 relative error = 1.310656164027645e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = -1.355148546374356 y[1] (numeric) = -1.355148546374526 absolute error = 1.691979889528739e-13 relative error = 1.248556768227041e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = -1.534274607258878 y[1] (numeric) = -1.534274607259061 absolute error = 1.825206652483757e-13 relative error = 1.189621886361436e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = -1.719103167610936 y[1] (numeric) = -1.71910316761113 absolute error = 1.940669847044774e-13 relative error = 1.128885039367214e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = -1.908786648496086 y[1] (numeric) = -1.90878664849629 absolute error = 2.047251257408789e-13 relative error = 1.07254064199464e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = -2.102428962218741 y[1] (numeric) = -2.102428962218955 absolute error = 2.144950883575802e-13 relative error = 1.020225140597467e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = -2.299094465734218 y[1] (numeric) = -2.29909446573444 absolute error = 2.224886941348814e-13 relative error = 9.677231512269742e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -2.497817309284757 y[1] (numeric) = -2.497817309284986 absolute error = 2.291500322826323e-13 relative error = 9.174010902672812e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -2.697611086851036 y[1] (numeric) = -2.69761108685127 absolute error = 2.34035013590983e-13 relative error = 8.67563952163971e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -2.897478691995048 y[1] (numeric) = -2.897478691995286 absolute error = 2.380318164796336e-13 relative error = 8.21513604697944e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -3.096422280618036 y[1] (numeric) = -3.096422280618277 absolute error = 2.406963517387339e-13 relative error = 7.773369712696025e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -3.293453241088881 y[1] (numeric) = -3.293453241089122 absolute error = 2.41140440948584e-13 relative error = 7.321811584877949e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = sin(x) - 1,0; Iterations = 981 Total Elapsed Time = 58 Seconds Elapsed Time(since restart) = 57 Seconds Time to Timeout = 9 Minutes 2 Seconds Percent Done = 100.2 %