##############ECHO OF PROBLEM################# ##############temp/sub_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 - 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(2.0 + cos(x) + x); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 3.095004165278026 y[1] (numeric) = 3.095004165278026 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) = 3.180066577841242 y[1] (numeric) = 3.180066577841226 absolute error = 1.554312234475219e-14 relative error = 4.887671991856062e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 3.255336489125606 y[1] (numeric) = 3.255336489125576 absolute error = 2.97539770599542e-14 relative error = 9.140061913521636e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 3.321060994002885 y[1] (numeric) = 3.321060994002841 absolute error = 4.39648317751562e-14 relative error = 1.323818859531552e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 3.377582561890373 y[1] (numeric) = 3.377582561890315 absolute error = 5.728750807065808e-14 relative error = 1.696109777360861e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 3.425335614909678 y[1] (numeric) = 3.425335614909609 absolute error = 6.972200594645983e-14 relative error = 2.035479549594393e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 3.464842187284489 y[1] (numeric) = 3.464842187284407 absolute error = 8.215650382226158e-14 relative error = 2.371147064757092e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 3.496706709347166 y[1] (numeric) = 3.496706709347073 absolute error = 9.281464485866309e-14 relative error = 2.654344575441718e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 3.521609968270665 y[1] (numeric) = 3.521609968270562 absolute error = 1.025846074753645e-13 relative error = 2.913003098004634e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 3.54030230586814 y[1] (numeric) = 3.540302305868028 absolute error = 1.119104808822158e-13 relative error = 3.161043075240251e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 3.554134433252361 y[1] (numeric) = 3.554134433252242 absolute error = 1.190159082398168e-13 relative error = 3.348660847668225e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 3.562693049001799 y[1] (numeric) = 3.562693049001675 absolute error = 1.243449787580175e-13 relative error = 3.490196237726871e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 3.567677714043213 y[1] (numeric) = 3.567677714043084 absolute error = 1.296740492762183e-13 relative error = 3.634690677518065e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 3.570037790195616 y[1] (numeric) = 3.570037790195483 absolute error = 1.323385845353187e-13 relative error = 3.70692391264764e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 3.570748863302624 y[1] (numeric) = 3.57074886330249 absolute error = 1.341149413747189e-13 relative error = 3.75593318121719e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 3.570802995501196 y[1] (numeric) = 3.570802995501062 absolute error = 1.34559030584569e-13 relative error = 3.768312918805601e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 3.571198812864694 y[1] (numeric) = 3.571198812864561 absolute error = 1.332267629550188e-13 relative error = 3.730589360499613e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 3.572931527461255 y[1] (numeric) = 3.572931527461126 absolute error = 1.296740492762183e-13 relative error = 3.629346050422582e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 3.576982993523786 y[1] (numeric) = 3.576982993523661 absolute error = 1.252331571777177e-13 relative error = 3.501083382405097e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 3.58431189708702 y[1] (numeric) = 3.584311897086901 absolute error = 1.190159082398168e-13 relative error = 3.320467405097791e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104999999999977 y[1] (analytic) = 3.595844177113562 y[1] (numeric) = 3.595844177113451 absolute error = 1.110223024625157e-13 relative error = 3.087517061199101e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204999999999975 y[1] (analytic) = 3.612463773817846 y[1] (numeric) = 3.612463773817744 absolute error = 1.016964290556643e-13 relative error = 2.815154294216938e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304999999999973 y[1] (analytic) = 3.635003796627706 y[1] (numeric) = 3.635003796627615 absolute error = 9.14823772291129e-14 relative error = 2.516706511117915e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = 3.664238200030363 y[1] (numeric) = 3.664238200030283 absolute error = 7.949196856316121e-14 relative error = 2.16939959204897e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = 3.700874050475019 y[1] (numeric) = 3.700874050474953 absolute error = 6.616929226765933e-14 relative error = 1.787936886400289e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = 3.74554446159863 y[1] (numeric) = 3.745544461598577 absolute error = 5.240252676230739e-14 relative error = 1.399063001375815e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = 3.798802268363717 y[1] (numeric) = 3.798802268363679 absolute error = 3.863576125695545e-14 relative error = 1.017051126317171e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = 3.86111450331417 y[1] (numeric) = 3.861114503314146 absolute error = 2.398081733190338e-14 relative error = 6.210853708513322e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = 3.932857730140443 y[1] (numeric) = 3.932857730140436 absolute error = 6.661338147750939e-15 relative error = 1.693765349481142e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = 4.014314281179642 y[1] (numeric) = 4.014314281179653 absolute error = 1.06581410364015e-14 relative error = 2.655034033177271e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = 4.105669436444134 y[1] (numeric) = 4.105669436444162 absolute error = 2.842170943040401e-14 relative error = 6.922551820201987e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = 4.207009572364909 y[1] (numeric) = 4.207009572364954 absolute error = 4.440892098500626e-14 relative error = 1.055593533152872e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = 4.318321298746839 y[1] (numeric) = 4.318321298746901 absolute error = 6.217248937900877e-14 relative error = 1.439737459948869e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = 4.439491592559073 y[1] (numeric) = 4.439491592559155 absolute error = 8.171241461241152e-14 relative error = 1.840580456315488e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = 4.57030892722381 y[1] (numeric) = 4.570308927223909 absolute error = 9.85878045867139e-14 relative error = 2.157136555900174e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = 4.710465386119935 y[1] (numeric) = 4.71046538612005 absolute error = 1.145750161413162e-13 relative error = 2.432350240359009e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = 4.859559739184118 y[1] (numeric) = 4.859559739184249 absolute error = 1.305622276959184e-13 relative error = 2.686708975777275e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = 5.017101451868979 y[1] (numeric) = 5.017101451869125 absolute error = 1.465494392505207e-13 relative error = 2.920998123247594e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = 5.182515586402131 y[1] (numeric) = 5.182515586402291 absolute error = 1.598721155460225e-13 relative error = 3.084836174260518e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = 5.355148546374356 y[1] (numeric) = 5.35514854637453 absolute error = 1.740829702612245e-13 relative error = 3.250758942608333e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = 5.534274607258878 y[1] (numeric) = 5.534274607259064 absolute error = 1.865174681370263e-13 relative error = 3.370224308934469e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = 5.719103167610935 y[1] (numeric) = 5.719103167611133 absolute error = 1.971756091734278e-13 relative error = 3.447666590281056e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = 5.908786648496085 y[1] (numeric) = 5.908786648496294 absolute error = 2.087219286295294e-13 relative error = 3.532399137861133e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = 6.102428962218741 y[1] (numeric) = 6.102428962218959 absolute error = 2.184918912462308e-13 relative error = 3.580408597936236e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = 6.299094465734218 y[1] (numeric) = 6.299094465734447 absolute error = 2.291500322826323e-13 relative error = 3.63782498467298e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = 6.497817309284757 y[1] (numeric) = 6.497817309284994 absolute error = 2.371436380599334e-13 relative error = 3.649589189297118e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = 6.697611086851036 y[1] (numeric) = 6.697611086851277 absolute error = 2.415845301584341e-13 relative error = 3.607025356141095e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = 6.897478691995047 y[1] (numeric) = 6.897478691995293 absolute error = 2.451372438372346e-13 relative error = 3.554012339635519e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = 7.096422280618036 y[1] (numeric) = 7.096422280618281 absolute error = 2.451372438372346e-13 relative error = 3.454377912469511e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = 7.293453241088881 y[1] (numeric) = 7.293453241089127 absolute error = 2.460254222569347e-13 relative error = 3.373236437177791e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = 1.0 - sin(x); Iterations = 981 Total Elapsed Time = 20 Seconds Elapsed Time(since restart) = 20 Seconds Time to Timeout = 9 Minutes 40 Seconds Percent Done = 100.2 %