##############ECHO OF PROBLEM################# ##############temp/expt_lin_sin_new_sm_hpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0 * x + 1.0 ) + ( 2.0 * sin ( x ) ) / ( 2.0 * 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=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_max_h=0.000001; glob_look_poles=true; 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*x+1.0,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 = 0.9 estimated_steps = 900000.0000000001 step_error = 3.513641844631533e-15 est_needed_step_err = 3.513641844631533e-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] = 0.1 y[1] (analytic) = 1.01836844605944 y[1] (numeric) = 1.01836844605944 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 1e-06 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] = 0.11000000000001 y[1] (analytic) = 1.022069516363144 y[1] (numeric) = 1.022069516363144 absolute error = 2.220446049250313e-16 relative error = 2.172500024412608e-14 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 16 h = 1e-06 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] = 0.12000000000002 y[1] (analytic) = 1.026085891407608 y[1] (numeric) = 1.026085891407602 absolute error = 5.773159728050814e-15 relative error = 5.626390321117332e-13 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 15 h = 1e-06 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] = 0.13000000000003 y[1] (analytic) = 1.030413285474386 y[1] (numeric) = 1.030413285474374 absolute error = 1.154631945610163e-14 relative error = 1.120552269547445e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.14000000000004 y[1] (analytic) = 1.035047815453387 y[1] (numeric) = 1.035047815453376 absolute error = 1.13242748511766e-14 relative error = 1.094082290895534e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.15000000000005 y[1] (analytic) = 1.039985973153431 y[1] (numeric) = 1.039985973153416 absolute error = 1.443289932012704e-14 relative error = 1.387797498495465e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.16000000000006 y[1] (analytic) = 1.045224599813314 y[1] (numeric) = 1.045224599813293 absolute error = 2.087219286295294e-14 relative error = 1.996909838008109e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.17000000000007 y[1] (analytic) = 1.050760862591659 y[1] (numeric) = 1.050760862591621 absolute error = 3.796962744218035e-14 relative error = 3.613536513772488e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.18000000000008 y[1] (analytic) = 1.056592232838128 y[1] (numeric) = 1.056592232838095 absolute error = 3.26405569239796e-14 relative error = 3.089229308103404e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.19000000000009 y[1] (analytic) = 1.062716465969892 y[1] (numeric) = 1.062716465969855 absolute error = 3.68594044175552e-14 relative error = 3.468413786542334e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.2000000000001 y[1] (analytic) = 1.069131582795989 y[1] (numeric) = 1.069131582795939 absolute error = 4.951594689828198e-14 relative error = 4.631417469567971e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.21000000000011 y[1] (analytic) = 1.07583585214866 y[1] (numeric) = 1.075835852148612 absolute error = 4.862776847858186e-14 relative error = 4.519998881006097e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.22000000000012 y[1] (analytic) = 1.082827774695303 y[1] (numeric) = 1.082827774695241 absolute error = 6.283862319378386e-14 relative error = 5.803196469675521e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.23000000000013 y[1] (analytic) = 1.090106067817514 y[1] (numeric) = 1.09010606781745 absolute error = 6.350475700855895e-14 relative error = 5.825557611627733e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.24000000000014 y[1] (analytic) = 1.097669651455056 y[1] (numeric) = 1.097669651454977 absolute error = 7.904787935331115e-14 relative error = 7.201427064010228e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.25000000000015 y[1] (analytic) = 1.105517634822684 y[1] (numeric) = 1.105517634822599 absolute error = 8.43769498715119e-14 relative error = 7.63234770877674e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 1e-06 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] = 0.2600009999998824 y[1] (analytic) = 1.113650131249449 y[1] (numeric) = 1.113650131249583 absolute error = 1.338928967697939e-13 relative error = 1.202288699230646e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2700009999996149 y[1] (analytic) = 1.122064965359962 y[1] (numeric) = 1.122064965360325 absolute error = 3.630429290524262e-13 relative error = 3.235489390188392e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2800009999993473 y[1] (analytic) = 1.130762541032839 y[1] (numeric) = 1.130762541033433 absolute error = 5.937472735695337e-13 relative error = 5.250857293408433e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.2900009999990797 y[1] (analytic) = 1.139742606473907 y[1] (numeric) = 1.139742606474744 absolute error = 8.37108160567368e-13 relative error = 7.344712357092464e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.3000009999988122 y[1] (analytic) = 1.149005043192053 y[1] (numeric) = 1.14900504319315 absolute error = 1.09712239293458e-12 relative error = 9.548455852610204e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 1e-06 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] = 0.3100009999985446 y[1] (analytic) = 1.158549856458415 y[1] (numeric) = 1.158549856459758 absolute error = 1.343147815191514e-12 relative error = 1.15933536023853e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3200009999982771 y[1] (analytic) = 1.168377166197088 y[1] (numeric) = 1.168377166198693 absolute error = 1.604716359793201e-12 relative error = 1.373457481214169e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3300009999980095 y[1] (analytic) = 1.178487198265083 y[1] (numeric) = 1.178487198266968 absolute error = 1.885158695813516e-12 relative error = 1.599642913888894e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.340000999997742 y[1] (analytic) = 1.188880276083007 y[1] (numeric) = 1.188880276085174 absolute error = 2.167377388673231e-12 relative error = 1.823040916966063e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3500009999974744 y[1] (analytic) = 1.199556812581258 y[1] (numeric) = 1.199556812583709 absolute error = 2.451150393767421e-12 relative error = 2.043379995060784e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3600009999972069 y[1] (analytic) = 1.210517302429568 y[1] (numeric) = 1.210517302432305 absolute error = 2.736255666491161e-12 relative error = 2.260401946340924e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3700009999969393 y[1] (analytic) = 1.221762314520449 y[1] (numeric) = 1.221762314523484 absolute error = 3.035349749325178e-12 relative error = 2.484402827989154e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3800009999966718 y[1] (analytic) = 1.23329248467961 y[1] (numeric) = 1.233292484682956 absolute error = 3.346212196220222e-12 relative error = 2.713234887739963e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.3900009999964042 y[1] (analytic) = 1.245108508578666 y[1] (numeric) = 1.245108508582328 absolute error = 3.661737579818691e-12 relative error = 2.940898367162144e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4000009999961366 y[1] (analytic) = 1.257211134827523 y[1] (numeric) = 1.257211134831515 absolute error = 3.992361996552063e-12 relative error = 3.17557002635025e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4100009999958691 y[1] (analytic) = 1.269601158225721 y[1] (numeric) = 1.269601158230041 absolute error = 4.319877788816484e-12 relative error = 3.402547139176803e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 1e-06 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] = 0.4200009999956015 y[1] (analytic) = 1.282279413153747 y[1] (numeric) = 1.282279413158399 absolute error = 4.652722651599106e-12 relative error = 3.628478008670361e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.430000999995334 y[1] (analytic) = 1.295246767086895 y[1] (numeric) = 1.295246767091893 absolute error = 4.997335878442755e-12 relative error = 3.858211427681946e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.4400009999950664 y[1] (analytic) = 1.308504114215767 y[1] (numeric) = 1.308504114221118 absolute error = 5.35194111250803e-12 relative error = 4.090121730886296e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.4500009999947989 y[1] (analytic) = 1.322052369158783 y[1] (numeric) = 1.322052369164503 absolute error = 5.719424933658956e-12 relative error = 4.32617123729993e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.4600009999945313 y[1] (analytic) = 1.335892460753402 y[1] (numeric) = 1.335892460759494 absolute error = 6.092237825328084e-12 relative error = 4.56042533685103e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.4700009999942638 y[1] (analytic) = 1.350025325913838 y[1] (numeric) = 1.350025325920312 absolute error = 6.474598635008988e-12 relative error = 4.795909017948465e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.4800009999939962 y[1] (analytic) = 1.364451903544196 y[1] (numeric) = 1.36445190355106 absolute error = 6.863842827442568e-12 relative error = 5.030476200453512e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.4900009999937286 y[1] (analytic) = 1.379173128496932 y[1] (numeric) = 1.379173128504183 absolute error = 7.250200440012122e-12 relative error = 5.25691828691125e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.5000009999934611 y[1] (analytic) = 1.394189925567487 y[1] (numeric) = 1.394189925575146 absolute error = 7.65920660228403e-12 relative error = 5.493660843350629e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.5100009999937487 y[1] (analytic) = 1.409503203517697 y[1] (numeric) = 1.409503203524932 absolute error = 7.234435273062445e-12 relative error = 5.132613572645642e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.5200009999940363 y[1] (analytic) = 1.42511384911632 y[1] (numeric) = 1.425113849123101 absolute error = 6.781464279015381e-12 relative error = 4.758542121543771e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.5300009999943238 y[1] (analytic) = 1.441022721198471 y[1] (numeric) = 1.441022721204798 absolute error = 6.326716928128917e-12 relative error = 4.390435233989307e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.5400009999946114 y[1] (analytic) = 1.457230644729748 y[1] (numeric) = 1.457230644735609 absolute error = 5.860423257786351e-12 relative error = 4.021616810613532e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.5500009999948989 y[1] (analytic) = 1.473738404874011 y[1] (numeric) = 1.4737384048794 absolute error = 5.38902256153051e-12 relative error = 3.656702263921264e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.5600009999951865 y[1] (analytic) = 1.490546741059545 y[1] (numeric) = 1.490546741064455 absolute error = 4.910516437917067e-12 relative error = 3.294439753312574e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.570000999995474 y[1] (analytic) = 1.507656341039772 y[1] (numeric) = 1.507656341044188 absolute error = 4.416467191958873e-12 relative error = 2.929359345189374e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.5800009999957616 y[1] (analytic) = 1.52506783494534 y[1] (numeric) = 1.525067834949255 absolute error = 3.915312518643077e-12 relative error = 2.567303846378352e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.5900009999960492 y[1] (analytic) = 1.542781789324994 y[1] (numeric) = 1.542781789328393 absolute error = 3.399058812192379e-12 relative error = 2.203201279475534e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.6000009999963367 y[1] (analytic) = 1.560798701173247 y[1] (numeric) = 1.560798701176135 absolute error = 2.887690087050032e-12 relative error = 1.850136141758297e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.6100009999966243 y[1] (analytic) = 1.579118991943439 y[1] (numeric) = 1.5791189919458 absolute error = 2.361000284167858e-12 relative error = 1.495137666137591e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.6200009999969118 y[1] (analytic) = 1.597743001545295 y[1] (numeric) = 1.597743001547109 absolute error = 1.814770556052281e-12 relative error = 1.135833832034991e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.6300009999971994 y[1] (analytic) = 1.616670982326681 y[1] (numeric) = 1.616670982327955 absolute error = 1.27453603226968e-12 relative error = 7.883706989256358e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 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] = 0.6400009999974869 y[1] (analytic) = 1.635903093039743 y[1] (numeric) = 1.635903093040464 absolute error = 7.212008767965017e-13 relative error = 4.4085794559897e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 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] = 0.6500009999977745 y[1] (analytic) = 1.655439392792149 y[1] (numeric) = 1.655439392792291 absolute error = 1.4210854715202e-13 relative error = 8.584340071328887e-12 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 14 h = 1e-06 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] = 0.6600009999980621 y[1] (analytic) = 1.675279834984666 y[1] (numeric) = 1.675279834984244 absolute error = 4.225508831723346e-13 relative error = 2.522270455050288e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 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] = 0.6700009999983496 y[1] (analytic) = 1.695424261236781 y[1] (numeric) = 1.695424261235772 absolute error = 1.009414773989192e-12 relative error = 5.953759168533088e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 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] = 0.6800009999986372 y[1] (analytic) = 1.715872395302577 y[1] (numeric) = 1.715872395300976 absolute error = 1.601163646114401e-12 relative error = 9.331484383674415e-11 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 13 h = 1e-06 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] = 0.6900009999989247 y[1] (analytic) = 1.736623836979554 y[1] (numeric) = 1.736623836977355 absolute error = 2.19912976717751e-12 relative error = 1.266324762075347e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.7000009999992123 y[1] (analytic) = 1.757678056013553 y[1] (numeric) = 1.757678056010745 absolute error = 2.808198118486871e-12 relative error = 1.59767490347801e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.7100009999994998 y[1] (analytic) = 1.779034386003409 y[1] (numeric) = 1.779034385999993 absolute error = 3.416378291376532e-12 relative error = 1.920355400803358e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.7200009999997874 y[1] (analytic) = 1.800692018309407 y[1] (numeric) = 1.800692018305374 absolute error = 4.032996159253344e-12 relative error = 2.239692361739767e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.7300000000000749 y[1] (analytic) = 1.822647785192286 y[1] (numeric) = 1.822647785187616 absolute error = 4.669598041573408e-12 relative error = 2.56198596322919e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.7400000000003625 y[1] (analytic) = 1.844904966992065 y[1] (numeric) = 1.844904966986756 absolute error = 5.308198325337798e-12 relative error = 2.877220464093764e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.75000000000065 y[1] (analytic) = 1.867460111133087 y[1] (numeric) = 1.867460111127129 absolute error = 5.958122883953365e-12 relative error = 3.19049539448436e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.7600000000009376 y[1] (analytic) = 1.890311779367246 y[1] (numeric) = 1.890311779360629 absolute error = 6.617817405185633e-12 relative error = 3.50091317073676e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.7700000000012251 y[1] (analytic) = 1.913458360982099 y[1] (numeric) = 1.91345836097482 absolute error = 7.279066238652376e-12 relative error = 3.804141436825587e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.7800000000015127 y[1] (analytic) = 1.93689806684274 y[1] (numeric) = 1.936898066834779 absolute error = 7.961853398796848e-12 relative error = 4.110620757536892e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.7900000000018003 y[1] (analytic) = 1.960628923478323 y[1] (numeric) = 1.960628923469683 absolute error = 8.639089443818193e-12 relative error = 4.406284810127004e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.8000000000020878 y[1] (analytic) = 1.984648767220717 y[1] (numeric) = 1.984648767211384 absolute error = 9.332756789603991e-12 relative error = 4.702472771881694e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.8100000000023754 y[1] (analytic) = 2.008955238403193 y[1] (numeric) = 2.008955238393161 absolute error = 1.003108707209321e-11 relative error = 4.99318595075636e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.8200000000026629 y[1] (analytic) = 2.033545775627385 y[1] (numeric) = 2.033545775616668 absolute error = 1.071631672289186e-11 relative error = 5.269769115271423e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.8300000000029505 y[1] (analytic) = 2.058417610107178 y[1] (numeric) = 2.058417610095743 absolute error = 1.143485306442926e-11 relative error = 5.555166749585801e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.840000000003238 y[1] (analytic) = 2.083567760098497 y[1] (numeric) = 2.083567760086328 absolute error = 1.216937661752127e-11 relative error = 5.840643558885735e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.8500000000035256 y[1] (analytic) = 2.108993025424345 y[1] (numeric) = 2.108993025411441 absolute error = 1.290390017061327e-11 relative error = 6.11851249153226e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.8600000000038132 y[1] (analytic) = 2.134689982104736 y[1] (numeric) = 2.13468998209108 absolute error = 1.365618729209928e-11 relative error = 6.39726958320885e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.8700000000041007 y[1] (analytic) = 2.160654977101538 y[1] (numeric) = 2.160654977087126 absolute error = 1.441247121647393e-11 relative error = 6.670417706304911e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.8800000000043883 y[1] (analytic) = 2.186884123188481 y[1] (numeric) = 2.186884123173302 absolute error = 1.517941328188499e-11 relative error = 6.941114584413086e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.8900000000046758 y[1] (analytic) = 2.213373293956924 y[1] (numeric) = 2.213373293940977 absolute error = 1.59476876149256e-11 relative error = 7.205150463533137e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9000000000049634 y[1] (analytic) = 2.240118118968215 y[1] (numeric) = 2.240118118951523 absolute error = 1.669242521984415e-11 relative error = 7.451582610086911e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9100000000052509 y[1] (analytic) = 2.267113979063737 y[1] (numeric) = 2.267113979046272 absolute error = 1.746514044498326e-11 relative error = 7.703688745369539e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9200000000055385 y[1] (analytic) = 2.294356001843965 y[1] (numeric) = 2.294356001825719 absolute error = 1.824584927589967e-11 relative error = 7.952492665146801e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9300000000058261 y[1] (analytic) = 2.321839057328068 y[1] (numeric) = 2.321839057309058 absolute error = 1.900968271684178e-11 relative error = 8.187338677435203e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9400000000061136 y[1] (analytic) = 2.34955775380578 y[1] (numeric) = 2.349557753785966 absolute error = 1.981437236509009e-11 relative error = 8.433234864303743e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9500000000064012 y[1] (analytic) = 2.377506433893429 y[1] (numeric) = 2.377506433872832 absolute error = 2.059730164205575e-11 relative error = 8.66340521666871e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9600000000066887 y[1] (analytic) = 2.405679170806153 y[1] (numeric) = 2.405679170784741 absolute error = 2.141176125292077e-11 relative error = 8.900505733582754e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9700000000069763 y[1] (analytic) = 2.434069764858455 y[1] (numeric) = 2.434069764836225 absolute error = 2.223021766667443e-11 relative error = 9.132941868643259e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9800000000072638 y[1] (analytic) = 2.462671740205331 y[1] (numeric) = 2.462671740182275 absolute error = 2.30557795077857e-11 relative error = 9.36210016600238e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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] = 0.9900000000075514 y[1] (analytic) = 2.491478341836276 y[1] (numeric) = 2.491478341812382 absolute error = 2.389421993598262e-11 relative error = 9.590378344758975e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 1e-06 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 * x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0 * x + 1.0 ) + ( 2.0 * sin ( x ) ) / ( 2.0 * x + 1.0 ) ) ; Iterations = 900000 Total Elapsed Time = 44.0 Seconds Elapsed Time(since restart) = 44.0 Seconds Time to Timeout = 9 Minutes 16.0 Seconds Percent Done = 100 %