##############ECHO OF PROBLEM################# ##############temp/div_lin_exppostode.ode################# diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(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(-(0.1 * (5.0 + 2.0*x))/exp(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -0.4705154573786989 y[1] (numeric) = -0.4705154573786989 absolute error = 0 relative error = 0 % Correct digits = 16 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] = 0.2000000000000001 y[1] (analytic) = -0.4421146066621102 y[1] (numeric) = -0.4421146066621015 absolute error = 8.715250743307479e-15 relative error = 1.971265054802449e-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] = 0.3000000000000002 y[1] (analytic) = -0.414858203581762 y[1] (numeric) = -0.4148582035817456 absolute error = 1.63202784619898e-14 relative error = 3.933941361430336e-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] = 0.4000000000000002 y[1] (analytic) = -0.3887856267006707 y[1] (numeric) = -0.3887856267006476 absolute error = 2.309263891220326e-14 relative error = 5.939684321195976e-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] = 0.5000000000000003 y[1] (analytic) = -0.36391839582758 y[1] (numeric) = -0.3639183958275509 absolute error = 2.90878432451791e-14 relative error = 7.992957646186306e-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] = 0.6000000000000004 y[1] (analytic) = -0.3402632143782963 y[1] (numeric) = -0.3402632143782622 absolute error = 3.408384685599231e-14 relative error = 1.001690615257009e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 81.88 Order of pole = 2.346e+04 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 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.7000000000000005 y[1] (analytic) = -0.317814594426502 y[1] (numeric) = -0.3178145944264634 absolute error = 3.863576125695545e-14 relative error = 1.215669825568391e-11 % Correct digits = 12 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 Complex estimate of poles used x[1] = 0.8000000000000006 y[1] (analytic) = -0.2965571163173661 y[1] (numeric) = -0.2965571163173236 absolute error = 4.257705299437475e-14 relative error = 1.435711728084452e-11 % Correct digits = 12 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 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 0.9000000000000007 y[1] (analytic) = -0.2764673686236073 y[1] (numeric) = -0.2764673686235612 absolute error = 4.601874437071274e-14 relative error = 1.664527159202081e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 108.4 Order of pole = 2.179e+04 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.000000000000001 y[1] (analytic) = -0.2575156088200095 y[1] (numeric) = -0.2575156088199605 absolute error = 4.901634653720066e-14 relative error = 1.903432058421772e-11 % Correct digits = 12 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] = 1.104999999999998 y[1] (analytic) = -0.2388030460964686 y[1] (numeric) = -0.2388030460964165 absolute error = 5.209721543053547e-14 relative error = 2.181597608662408e-11 % Correct digits = 12 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 Complex estimate of poles used Complex estimate of poles used x[1] = 1.204999999999996 y[1] (analytic) = -0.2220717716393162 y[1] (numeric) = -0.2220717716392615 absolute error = 5.470623953840459e-14 relative error = 2.463448601979778e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 208.8 Order of pole = 4.812e+04 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] = 1.304999999999994 y[1] (analytic) = -0.2063622991697024 y[1] (numeric) = -0.2063622991696454 absolute error = 5.698219673888616e-14 relative error = 2.761269716811342e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 1.404999999999992 y[1] (analytic) = -0.1916316710897366 y[1] (numeric) = -0.1916316710896776 absolute error = 5.90361093344427e-14 relative error = 3.080707327694151e-11 % Correct digits = 12 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 Complex estimate of poles used x[1] = 1.50499999999999 y[1] (analytic) = -0.1778358523593928 y[1] (numeric) = -0.1778358523593321 absolute error = 6.072919944699606e-14 relative error = 3.414901924515588e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 262.9 Order of pole = 5.724e+04 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 Complex estimate of poles used x[1] = 1.604999999999988 y[1] (analytic) = -0.1649303245813021 y[1] (numeric) = -0.1649303245812398 absolute error = 6.228351168147128e-14 relative error = 3.776352944165143e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 119.6 Order of pole = 1.276e+04 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.704999999999986 y[1] (analytic) = -0.1528705767734858 y[1] (numeric) = -0.1528705767734221 absolute error = 6.361577931102147e-14 relative error = 4.161414227231146e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 108.1 Order of pole = 1.007e+04 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] = 1.804999999999984 y[1] (analytic) = -0.1416125071129322 y[1] (numeric) = -0.1416125071128674 absolute error = 6.472600233564663e-14 relative error = 4.570641651307634e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 1.904999999999981 y[1] (analytic) = -0.1311127481501076 y[1] (numeric) = -0.1311127481500418 absolute error = 6.57529586334249e-14 relative error = 5.014993550295052e-11 % Correct digits = 12 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] = 2.004999999999979 y[1] (analytic) = -0.1213289264216527 y[1] (numeric) = -0.1213289264215861 absolute error = 6.657174811408595e-14 relative error = 5.486881824267536e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.104999999999977 y[1] (analytic) = -0.112219866001825 y[1] (numeric) = -0.1122198660017577 absolute error = 6.734890423132356e-14 relative error = 6.001513513679323e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used Complex estimate of poles used x[1] = 2.204999999999975 y[1] (analytic) = -0.1037457443115226 y[1] (numeric) = -0.1037457443114546 absolute error = 6.801503804609865e-14 relative error = 6.555935233532706e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.304999999999973 y[1] (analytic) = -0.09586820742812956 y[1] (numeric) = -0.09586820742806096 absolute error = 6.859790513402686e-14 relative error = 7.155438385082282e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.404999999999971 y[1] (analytic) = -0.08855045119320043 y[1] (numeric) = -0.08855045119313135 absolute error = 6.908362770730037e-14 relative error = 7.80161216305639e-11 % Correct digits = 12 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] = 2.504999999999969 y[1] (analytic) = -0.0817572735832808 y[1] (numeric) = -0.08175727358321126 absolute error = 6.954159470495824e-14 relative error = 8.505860293166546e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.604999999999967 y[1] (analytic) = -0.07545510307870666 y[1] (numeric) = -0.07545510307863679 absolute error = 6.987466161234579e-14 relative error = 9.260428885699095e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -0.06961200712430615 y[1] (numeric) = -0.06961200712423597 absolute error = 7.017997294411771e-14 relative error = 1.008159020882667e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 458.1 Order of pole = 8.323e+04 x[1] = 2.804999999999962 y[1] (analytic) = -0.06419768421410978 y[1] (numeric) = -0.06419768421403931 absolute error = 7.047140648808181e-14 relative error = 1.097725055829867e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -0.05918344264021291 y[1] (numeric) = -0.05918344264014223 absolute error = 7.067263441129512e-14 relative error = 1.194128480171847e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -0.05454216851561858 y[1] (numeric) = -0.05454216851554772 absolute error = 7.086692344060452e-14 relative error = 1.299305204931689e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.104999999999956 y[1] (analytic) = -0.05024828530493999 y[1] (numeric) = -0.05024828530486897 absolute error = 7.101957910649048e-14 relative error = 1.413373186278825e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -0.0462777067688137 y[1] (numeric) = -0.04627770676874255 absolute error = 7.115141809066472e-14 relative error = 1.537487984141282e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -0.04260778494204648 y[1] (numeric) = -0.04260778494197522 absolute error = 7.125550149922333e-14 relative error = 1.672358739045984e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -0.03921725451683269 y[1] (numeric) = -0.03921725451676136 absolute error = 7.133182933216631e-14 relative error = 1.818888910276713e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = -0.03608617478635352 y[1] (numeric) = -0.03608617478628211 absolute error = 7.141509605901319e-14 relative error = 1.979015411908379e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = -0.03319587011673962 y[1] (numeric) = -0.03319587011666816 absolute error = 7.146366831634055e-14 relative error = 2.152787924070823e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.704999999999943 y[1] (analytic) = -0.03052886975324059 y[1] (numeric) = -0.0305288697531691 absolute error = 7.149489333890813e-14 relative error = 2.341878160468717e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -0.02806884762639954 y[1] (numeric) = -0.02806884762632801 absolute error = 7.153305725537962e-14 relative error = 2.548485716531546e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.904999999999939 y[1] (analytic) = -0.02580056270334197 y[1] (numeric) = -0.02580056270327041 absolute error = 7.156081283099525e-14 relative error = 2.773614422825201e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = -0.02370980032554044 y[1] (numeric) = -0.02370980032546887 absolute error = 7.157122117185111e-14 relative error = 3.018634496670723e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = -0.02178331488547747 y[1] (numeric) = -0.02178331488540587 absolute error = 7.159550730051478e-14 relative error = 3.286713141545146e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = -0.02000877411862113 y[1] (numeric) = -0.02000877411854952 absolute error = 7.160591564137064e-14 relative error = 3.578725773845922e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.30499999999993 y[1] (analytic) = -0.01837470522239397 y[1] (numeric) = -0.01837470522232236 absolute error = 7.16093850883226e-14 relative error = 3.897171912235602e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = -0.01687044295889974 y[1] (numeric) = -0.01687044295882813 absolute error = 7.160591564137064e-14 relative error = 4.244459722594069e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = -0.015486079851791 y[1] (numeric) = -0.0154860798517194 absolute error = 7.160591564137064e-14 relative error = 4.623889087921062e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -0.01421241854868742 y[1] (numeric) = -0.01421241854861582 absolute error = 7.160244619441869e-14 relative error = 5.038019809867723e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.704999999999922 y[1] (analytic) = -0.0130409263879988 y[1] (numeric) = -0.01304092638792721 absolute error = 7.159203785356283e-14 relative error = 5.489796945671513e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -0.01196369218200136 y[1] (numeric) = -0.01196369218192978 absolute error = 7.157989478923099e-14 relative error = 5.983093989739936e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.904999999999918 y[1] (analytic) = -0.01097338520579743 y[1] (numeric) = -0.01097338520572586 absolute error = 7.157122117185111e-14 relative error = 6.522255423425652e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 5.004999999999916 y[1] (analytic) = -0.01006321636369235 y[1] (numeric) = -0.01006321636362079 absolute error = 7.155907810751927e-14 relative error = 7.110954939387105e-10 % Correct digits = 11 h = 0.005 Finished! diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x); Iterations = 981 Total Elapsed Time = 31 Seconds Elapsed Time(since restart) = 31 Seconds Time to Timeout = 9 Minutes 29 Seconds Percent Done = 100.2 %