##############ECHO OF PROBLEM################# ##############temp/expt_c_sin_new_sm_hpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) * cos ( x ) * ln ( 2.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=1.4; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.0000001; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(expt(2.0,sin(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.3999999999999999 estimated_steps = 399999.9999999999 step_error = 5.2704627669473e-15 est_needed_step_err = 5.2704627669473e-15 opt_iter = 1 SETTING H FOR MAX H NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 1.979930418515512 y[1] (numeric) = 1.979930418515512 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.389999999994161 y[1] (analytic) = 1.977531690958136 y[1] (numeric) = 1.977531690944983 absolute error = 1.315325626194408e-11 relative error = 6.651350429469568e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.379999999988323 y[1] (analytic) = 1.975001200693339 y[1] (numeric) = 1.97500120066546 absolute error = 2.787903241596723e-11 relative error = 1.411595719849694e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.369999999982484 y[1] (analytic) = 1.972339713718799 y[1] (numeric) = 1.972339713674528 absolute error = 4.427125332995274e-11 relative error = 2.244605887212013e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.359999999976645 y[1] (analytic) = 1.969548034160331 y[1] (numeric) = 1.969548034097927 absolute error = 6.24034157681308e-11 relative error = 3.16841299048261e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.349999999970807 y[1] (analytic) = 1.966627003797494 y[1] (numeric) = 1.966627003715097 absolute error = 8.239653404018554e-11 relative error = 4.189738770040301e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.339999999964968 y[1] (analytic) = 1.963577501568239 y[1] (numeric) = 1.963577501463941 absolute error = 1.042987918253857e-10 relative error = 5.311671769618769e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.329999999959129 y[1] (analytic) = 1.960400443053048 y[1] (numeric) = 1.960400442924871 absolute error = 1.281763584159989e-10 relative error = 6.538274303610252e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.319999999953291 y[1] (analytic) = 1.957096779939047 y[1] (numeric) = 1.957096779784919 absolute error = 1.541284877504268e-10 relative error = 7.87536361667444e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.309999999947452 y[1] (analytic) = 1.953667499464617 y[1] (numeric) = 1.953667499282422 absolute error = 1.821944817237409e-10 relative error = 9.325767141730591e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299999999941613 y[1] (analytic) = 1.950113623844986 y[1] (numeric) = 1.950113623632497 absolute error = 2.124886933074777e-10 relative error = 1.08962211590789e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.289999999935775 y[1] (analytic) = 1.946436209679369 y[1] (numeric) = 1.94643620943433 absolute error = 2.450388780772528e-10 relative error = 1.258910396645454e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.279999999929936 y[1] (analytic) = 1.942636347340183 y[1] (numeric) = 1.94263634706021 absolute error = 2.79973155770108e-10 relative error = 1.441202086810747e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.269999999924097 y[1] (analytic) = 1.938715160344907 y[1] (numeric) = 1.938715160027615 absolute error = 3.17291970475253e-10 relative error = 1.636609528646824e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.259999999918259 y[1] (analytic) = 1.934673804711169 y[1] (numeric) = 1.934673804354092 absolute error = 3.570777007411152e-10 relative error = 1.845673931551598e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24999999991242 y[1] (analytic) = 1.930513468295639 y[1] (numeric) = 1.930513467896227 absolute error = 3.994120589823069e-10 relative error = 2.068942100336287e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.239999999906581 y[1] (analytic) = 1.926235370117341 y[1] (numeric) = 1.926235369672935 absolute error = 4.444054013674759e-10 relative error = 2.307118892435268e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.229999999900742 y[1] (analytic) = 1.921840759665985 y[1] (numeric) = 1.921840759173938 absolute error = 4.920475138447955e-10 relative error = 2.560292840965206e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.219999999894904 y[1] (analytic) = 1.917330916195963 y[1] (numeric) = 1.917330915653566 absolute error = 5.423967941453611e-10 relative error = 2.828915914116126e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.209999999889065 y[1] (analytic) = 1.91270714800661 y[1] (numeric) = 1.912707147411097 absolute error = 5.955136384017123e-10 relative error = 3.113459574939876e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.199999999883226 y[1] (analytic) = 1.907970791709414 y[1] (numeric) = 1.907970791057925 absolute error = 6.514886408126586e-10 relative error = 3.41456296733436e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.189999999877388 y[1] (analytic) = 1.903123211482783 y[1] (numeric) = 1.903123210772467 absolute error = 7.10315140040052e-10 relative error = 3.732365491389406e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.179999999871549 y[1] (analytic) = 1.898165798315063 y[1] (numeric) = 1.898165797542958 absolute error = 7.721043804309602e-10 relative error = 4.067634034478606e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.16999999986571 y[1] (analytic) = 1.89309996923645 y[1] (numeric) = 1.893099968399623 absolute error = 8.368266080083231e-10 relative error = 4.420403684998437e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.159999999859872 y[1] (analytic) = 1.887927166540474 y[1] (numeric) = 1.887927165635942 absolute error = 9.045328930312735e-10 relative error = 4.7911429480025e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.149999999854033 y[1] (analytic) = 1.88264885699573 y[1] (numeric) = 1.882648856020426 absolute error = 9.753047258698189e-10 relative error = 5.180491955500286e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.139999999848194 y[1] (analytic) = 1.877266531048531 y[1] (numeric) = 1.877266529999301 absolute error = 1.04923003618751e-09 relative error = 5.589137284631987e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.129999999842356 y[1] (analytic) = 1.871781702017173 y[1] (numeric) = 1.871781700890878 absolute error = 1.126294835174235e-09 relative error = 6.017233921885522e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.119999999836517 y[1] (analytic) = 1.866195905278495 y[1] (numeric) = 1.866195904071966 absolute error = 1.206529764985476e-09 relative error = 6.465182790149908e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.109999999830678 y[1] (analytic) = 1.860510697447412 y[1] (numeric) = 1.860510696157456 absolute error = 1.289955919858699e-09 relative error = 6.933343203178005e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09999999982484 y[1] (analytic) = 1.85472765555012 y[1] (numeric) = 1.854727654173538 absolute error = 1.376581515444286e-09 relative error = 7.42201428508913e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.089999999819001 y[1] (analytic) = 1.848848376191656 y[1] (numeric) = 1.848848374725177 absolute error = 1.466478938283444e-09 relative error = 7.931850751894353e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.079999999813162 y[1] (analytic) = 1.842874474718498 y[1] (numeric) = 1.842874473158826 absolute error = 1.559672613282714e-09 relative error = 8.463260166002118e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.069999999807324 y[1] (analytic) = 1.836807584376893 y[1] (numeric) = 1.836807582720716 absolute error = 1.656176529252207e-09 relative error = 9.01660328136133e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.059999999801485 y[1] (analytic) = 1.83064935546759 y[1] (numeric) = 1.830649353711606 absolute error = 1.755984024853774e-09 relative error = 9.5921374544458e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.049999999795646 y[1] (analytic) = 1.824401454497675 y[1] (numeric) = 1.824401452638557 absolute error = 1.859117970681723e-09 relative error = 1.019028989534327e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.039999999789808 y[1] (analytic) = 1.818065563330153 y[1] (numeric) = 1.818065561364504 absolute error = 1.96564942100963e-09 relative error = 1.081176312150782e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.029999999783969 y[1] (analytic) = 1.811643378331983 y[1] (numeric) = 1.811643376256468 absolute error = 2.075515315169696e-09 relative error = 1.145653355397498e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01999999977813 y[1] (analytic) = 1.805136609521206 y[1] (numeric) = 1.805136607332474 absolute error = 2.188731862418081e-09 relative error = 1.212502062654759e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.009999999772292 y[1] (analytic) = 1.798546979713841 y[1] (numeric) = 1.798546977408432 absolute error = 2.305409196878827e-09 relative error = 1.281817613263364e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = -1e-07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt ( 2.0 , sin ( x ) ) * cos ( x ) * ln ( 2.0 ) ; Iterations = 4000000 Total Elapsed Time = 1 Minutes 56.0 Seconds Elapsed Time(since restart) = 1 Minutes 56.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 1 Minutes 56.0 Seconds Time to Timeout = 8 Minutes 4.0 Seconds Percent Done = 0 %