##############ECHO OF PROBLEM################# ##############temp/div_exp_exppostode.ode################# diff ( y , x , 1 ) = exp(0.1 * x) / exp(0.2 * 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(- 10.0 * (exp(0.1* x)/exp(0.2*x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = -9.90049833749168 y[1] (numeric) = -9.90049833749168 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) = -9.801986733067553 y[1] (numeric) = -9.801986733067555 absolute error = 1.77635683940025e-15 relative error = 1.812241627921828e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 0.3000000000000002 y[1] (analytic) = -9.704455335485083 y[1] (numeric) = -9.704455335485084 absolute error = 1.77635683940025e-15 relative error = 1.830454959079327e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = -9.607894391523232 y[1] (numeric) = -9.607894391523232 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = -9.512294245007141 y[1] (numeric) = -9.512294245007142 absolute error = 1.77635683940025e-15 relative error = 1.86743260211135e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = -9.417645335842487 y[1] (numeric) = -9.417645335842488 absolute error = 1.77635683940025e-15 relative error = 1.886200611780992e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = -9.323938199059482 y[1] (numeric) = -9.323938199059485 absolute error = 3.552713678800501e-15 relative error = 3.810314486167302e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 0.8000000000000006 y[1] (analytic) = -9.231163463866356 y[1] (numeric) = -9.231163463866359 absolute error = 3.552713678800501e-15 relative error = 3.84860878339651e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = -9.139311852712281 y[1] (numeric) = -9.139311852712282 absolute error = 1.77635683940025e-15 relative error = 1.943643972355621e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = -9.048374180359595 y[1] (numeric) = -9.048374180359593 absolute error = 1.77635683940025e-15 relative error = 1.963177919029931e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = -8.953863301894861 y[1] (numeric) = -8.953863301894858 absolute error = 3.552713678800501e-15 relative error = 3.967799774259071e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 1.204999999999996 y[1] (analytic) = -8.864770873453788 y[1] (numeric) = -8.864770873453779 absolute error = 8.881784197001252e-15 relative error = 1.001919206236724e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = -8.776564929487391 y[1] (numeric) = -8.776564929487384 absolute error = 7.105427357601002e-15 relative error = 8.095909293313923e-14 % Correct digits = 15 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) = -8.689236649327771 y[1] (numeric) = -8.689236649327762 absolute error = 8.881784197001252e-15 relative error = 1.022159316801249e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = -8.602777300074139 y[1] (numeric) = -8.602777300074132 absolute error = 7.105427357601002e-15 relative error = 8.259457509773927e-14 % Correct digits = 15 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = -8.517178235719522 y[1] (numeric) = -8.517178235719511 absolute error = 1.06581410364015e-14 relative error = 1.251369965665761e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = -8.432430896286146 y[1] (numeric) = -8.432430896286135 absolute error = 1.06581410364015e-14 relative error = 1.263946442904811e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 1.804999999999984 y[1] (analytic) = -8.348526806969449 y[1] (numeric) = -8.348526806969438 absolute error = 1.06581410364015e-14 relative error = 1.276649315841444e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = -8.265457577290578 y[1] (numeric) = -8.265457577290565 absolute error = 1.243449787580175e-14 relative error = 1.504393163902462e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = -8.18321490025734 y[1] (numeric) = -8.183214900257328 absolute error = 1.243449787580175e-14 relative error = 1.519512566559962e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.104999999999977 y[1] (analytic) = -8.101790551533496 y[1] (numeric) = -8.10179055153348 absolute error = 1.598721155460225e-14 relative error = 1.973293613666206e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.204999999999975 y[1] (analytic) = -8.021176388616318 y[1] (numeric) = -8.021176388616295 absolute error = 2.309263891220326e-14 relative error = 2.878959119385083e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 2.304999999999973 y[1] (analytic) = -7.941364350022341 y[1] (numeric) = -7.941364350022315 absolute error = 2.575717417130363e-14 relative error = 3.243419271051475e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404999999999971 y[1] (analytic) = -7.862346454481189 y[1] (numeric) = -7.862346454481165 absolute error = 2.398081733190338e-14 relative error = 3.050084026535791e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504999999999969 y[1] (analytic) = -7.784114800137464 y[1] (numeric) = -7.784114800137438 absolute error = 2.664535259100376e-14 relative error = 3.423042089581362e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.604999999999967 y[1] (analytic) = -7.706661563760537 y[1] (numeric) = -7.706661563760507 absolute error = 3.019806626980426e-14 relative error = 3.918436799120167e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.704999999999965 y[1] (analytic) = -7.629978999962225 y[1] (numeric) = -7.629978999962194 absolute error = 3.019806626980426e-14 relative error = 3.957817743660076e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.804999999999962 y[1] (analytic) = -7.554059440422246 y[1] (numeric) = -7.554059440422212 absolute error = 3.375077994860476e-14 relative error = 4.467899705422255e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.90499999999996 y[1] (analytic) = -7.478895293121379 y[1] (numeric) = -7.478895293121342 absolute error = 3.730349362740526e-14 relative error = 4.987834722290427e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.004999999999958 y[1] (analytic) = -7.404479041582258 y[1] (numeric) = -7.404479041582219 absolute error = 3.907985046680551e-14 relative error = 5.277866308668025e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 3.104999999999956 y[1] (analytic) = -7.330803244117716 y[1] (numeric) = -7.330803244117673 absolute error = 4.263256414560601e-14 relative error = 5.81553790572877e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.204999999999954 y[1] (analytic) = -7.257860533086608 y[1] (numeric) = -7.257860533086564 absolute error = 4.352074256530614e-14 relative error = 5.996359721560773e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.304999999999952 y[1] (analytic) = -7.185643614157047 y[1] (numeric) = -7.185643614157 absolute error = 4.707345624410664e-14 relative error = 6.551042435692639e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.40499999999995 y[1] (analytic) = -7.114145265576956 y[1] (numeric) = -7.114145265576909 absolute error = 4.707345624410664e-14 relative error = 6.616881506746824e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.504999999999947 y[1] (analytic) = -7.043358337451899 y[1] (numeric) = -7.043358337451849 absolute error = 4.973799150320701e-14 relative error = 7.061686928341191e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.604999999999945 y[1] (analytic) = -6.97327575103007 y[1] (numeric) = -6.973275751030017 absolute error = 5.329070518200751e-14 relative error = 7.642133637714754e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 3.704999999999943 y[1] (analytic) = -6.903890497994428 y[1] (numeric) = -6.903890497994373 absolute error = 5.506706202140776e-14 relative error = 7.976236302908437e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 3.804999999999941 y[1] (analytic) = -6.835195639761846 y[1] (numeric) = -6.835195639761789 absolute error = 5.684341886080801e-14 relative error = 8.31628264305081e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 3.904999999999939 y[1] (analytic) = -6.767184306789256 y[1] (numeric) = -6.767184306789197 absolute error = 5.861977570020827e-14 relative error = 8.66235838166803e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.004999999999937 y[1] (analytic) = -6.699849697886681 y[1] (numeric) = -6.699849697886622 absolute error = 5.950795411990839e-14 relative error = 8.881983447879264e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.104999999999935 y[1] (analytic) = -6.633185079537125 y[1] (numeric) = -6.633185079537064 absolute error = 6.128431095930864e-14 relative error = 9.239047339168344e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.204999999999933 y[1] (analytic) = -6.567183785223193 y[1] (numeric) = -6.567183785223132 absolute error = 6.128431095930864e-14 relative error = 9.331901308625524e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.30499999999993 y[1] (analytic) = -6.501839214760457 y[1] (numeric) = -6.501839214760393 absolute error = 6.394884621840902e-14 relative error = 9.83550101842453e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.404999999999928 y[1] (analytic) = -6.437144833637413 y[1] (numeric) = -6.437144833637347 absolute error = 6.661338147750939e-14 relative error = 1.034828067397521e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.504999999999926 y[1] (analytic) = -6.373094172362038 y[1] (numeric) = -6.373094172361971 absolute error = 6.661338147750939e-14 relative error = 1.045228262378252e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.604999999999924 y[1] (analytic) = -6.309680825814828 y[1] (numeric) = -6.309680825814761 absolute error = 6.750155989720952e-14 relative error = 1.069809420803665e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.704999999999922 y[1] (analytic) = -6.246898452608286 y[1] (numeric) = -6.246898452608217 absolute error = 6.838973831690964e-14 relative error = 1.094779094549787e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 4.80499999999992 y[1] (analytic) = -6.184740774452769 y[1] (numeric) = -6.184740774452701 absolute error = 6.838973831690964e-14 relative error = 1.105781807370266e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 4.904999999999918 y[1] (analytic) = -6.123201575528667 y[1] (numeric) = -6.123201575528594 absolute error = 7.283063041541027e-14 relative error = 1.189420755091215e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE Complex estimate of poles used x[1] = 5.004999999999916 y[1] (analytic) = -6.062274701864802 y[1] (numeric) = -6.062274701864728 absolute error = 7.371880883511039e-14 relative error = 1.21602554256464e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = exp(0.1 * x) / exp(0.2 * x); Iterations = 981 Total Elapsed Time = 1 Minutes 45 Seconds Elapsed Time(since restart) = 1 Minutes 44 Seconds Time to Timeout = 8 Minutes 15 Seconds Percent Done = 100.2 %