##############ECHO OF PROBLEM################# ##############temp/expt_lin_sin_newpostode.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_look_poles=true; glob_max_iter=1000000; glob_max_h=0.00001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; 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 = 1.111111111111111e-16 est_needed_step_err = 1.111111111111111e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.031890051472423e-152 estimated_step_error = 1.031890051472423e-152 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.668123813664462e-144 estimated_step_error = 1.668123813664462e-144 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.119457130919725e-136 estimated_step_error = 1.119457130919725e-136 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.512525334680389e-129 estimated_step_error = 7.512525334680389e-129 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.041537794430847e-121 estimated_step_error = 5.041537794430847e-121 best_h = 1e-05 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 % Correct digits = 16 h = 1e-05 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] = 0.1100099999999961 y[1] (analytic) = 1.022073375992747 y[1] (numeric) = 1.022073375994517 absolute error = 1.769473456647574e-12 relative error = 1.731258731721558e-10 % Correct digits = 12 h = 1e-05 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] = 0.1200099999999922 y[1] (analytic) = 1.026090064127418 y[1] (numeric) = 1.026090064129188 absolute error = 1.770805724277125e-12 relative error = 1.725780013066407e-10 % Correct digits = 12 h = 1e-05 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] = 0.1300099999999953 y[1] (analytic) = 1.030417767205002 y[1] (numeric) = 1.030417767206771 absolute error = 1.768807322832799e-12 relative error = 1.71659241438613e-10 % Correct digits = 12 h = 1e-05 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] = 0.1400000000000053 y[1] (analytic) = 1.035047815453371 y[1] (numeric) = 1.035047815455137 absolute error = 1.766586876783549e-12 relative error = 1.70676837379706e-10 % Correct digits = 12 h = 1e-05 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] = 0.1500000000000153 y[1] (analytic) = 1.039985973153413 y[1] (numeric) = 1.039985973155176 absolute error = 1.762812118499824e-12 relative error = 1.695034513931644e-10 % Correct digits = 12 h = 1e-05 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] = 0.1600000000000253 y[1] (analytic) = 1.045224599813295 y[1] (numeric) = 1.045224599815054 absolute error = 1.759481449425948e-12 relative error = 1.683352505997504e-10 % Correct digits = 12 h = 1e-05 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] = 0.1700000000000353 y[1] (analytic) = 1.050760862591639 y[1] (numeric) = 1.05076086259339 absolute error = 1.751265799043722e-12 relative error = 1.666664472755798e-10 % Correct digits = 12 h = 1e-05 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] = 0.1800000000000453 y[1] (analytic) = 1.056592232838107 y[1] (numeric) = 1.056592232839851 absolute error = 1.744160371686121e-12 relative error = 1.650741239126035e-10 % Correct digits = 12 h = 1e-05 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] = 0.1900000000000553 y[1] (analytic) = 1.06271646596987 y[1] (numeric) = 1.062716465971608 absolute error = 1.738165167353145e-12 relative error = 1.63558693500325e-10 % Correct digits = 12 h = 1e-05 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] = 0.2000000000000653 y[1] (analytic) = 1.069131582795966 y[1] (numeric) = 1.0691315827977 absolute error = 1.733724275254644e-12 relative error = 1.621619174994954e-10 % Correct digits = 12 h = 1e-05 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] = 0.2100000000000753 y[1] (analytic) = 1.075835852148637 y[1] (numeric) = 1.075835852150367 absolute error = 1.729949516970919e-12 relative error = 1.608005081366177e-10 % Correct digits = 12 h = 1e-05 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] = 0.2200000000000853 y[1] (analytic) = 1.082827774695279 y[1] (numeric) = 1.082827774697001 absolute error = 1.722177955798543e-12 relative error = 1.590444940593794e-10 % Correct digits = 12 h = 1e-05 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] = 0.2300000000000953 y[1] (analytic) = 1.090106067817488 y[1] (numeric) = 1.090106067819202 absolute error = 1.714184350021242e-12 relative error = 1.572493173488362e-10 % Correct digits = 12 h = 1e-05 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] = 0.2400000000001053 y[1] (analytic) = 1.097669651455029 y[1] (numeric) = 1.097669651456736 absolute error = 1.707078922663641e-12 relative error = 1.555184586182921e-10 % Correct digits = 12 h = 1e-05 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] = 0.2500000000001153 y[1] (analytic) = 1.105517634822656 y[1] (numeric) = 1.105517634824356 absolute error = 1.700195539910965e-12 relative error = 1.537918063318552e-10 % Correct digits = 12 h = 1e-05 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] = 0.2600000000001253 y[1] (analytic) = 1.113649303916657 y[1] (numeric) = 1.113649303918348 absolute error = 1.691091711109038e-12 relative error = 1.518513687532997e-10 % Correct digits = 12 h = 1e-05 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] = 0.2700000000001353 y[1] (analytic) = 1.122064109735975 y[1] (numeric) = 1.122064109737654 absolute error = 1.679101302443087e-12 relative error = 1.496439720220785e-10 % Correct digits = 12 h = 1e-05 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] = 0.2800000000001453 y[1] (analytic) = 1.130761657149848 y[1] (numeric) = 1.130761657151516 absolute error = 1.667999072196835e-12 relative error = 1.47511110024824e-10 % Correct digits = 12 h = 1e-05 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] = 0.2900000000001553 y[1] (analytic) = 1.13974169435028 y[1] (numeric) = 1.139741694351941 absolute error = 1.661115689444159e-12 relative error = 1.457449260370433e-10 % Correct digits = 12 h = 1e-05 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] = 0.3000000000001653 y[1] (analytic) = 1.149004102833311 y[1] (numeric) = 1.149004102834961 absolute error = 1.650235503802833e-12 relative error = 1.436231167263497e-10 % Correct digits = 12 h = 1e-05 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] = 0.3100000000001753 y[1] (analytic) = 1.158548887858167 y[1] (numeric) = 1.15854888785981 absolute error = 1.643130076445232e-12 relative error = 1.418265637009863e-10 % Correct digits = 12 h = 1e-05 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] = 0.3200000000001853 y[1] (analytic) = 1.168376169337918 y[1] (numeric) = 1.168376169339554 absolute error = 1.635580559877781e-12 relative error = 1.399874974174295e-10 % Correct digits = 12 h = 1e-05 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] = 0.3300000000001953 y[1] (analytic) = 1.178486173119407 y[1] (numeric) = 1.178486173121033 absolute error = 1.625588552656154e-12 relative error = 1.379387038842623e-10 % Correct digits = 12 h = 1e-05 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] = 0.3400000000002053 y[1] (analytic) = 1.188879222613892 y[1] (numeric) = 1.188879222615507 absolute error = 1.615596545434528e-12 relative error = 1.358924030888897e-10 % Correct digits = 12 h = 1e-05 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] = 0.3500000000002153 y[1] (analytic) = 1.199555730743213 y[1] (numeric) = 1.199555730744818 absolute error = 1.604716359793201e-12 relative error = 1.337758904122746e-10 % Correct digits = 12 h = 1e-05 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] = 0.3600000000002253 y[1] (analytic) = 1.210516192169308 y[1] (numeric) = 1.210516192170897 absolute error = 1.588951192843524e-12 relative error = 1.312622832410065e-10 % Correct digits = 12 h = 1e-05 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] = 0.3700000000002353 y[1] (analytic) = 1.221761175777635 y[1] (numeric) = 1.221761175779215 absolute error = 1.580513497856373e-12 relative error = 1.29363539224464e-10 % Correct digits = 12 h = 1e-05 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] = 0.3800000000002453 y[1] (analytic) = 1.233291317387566 y[1] (numeric) = 1.233291317389135 absolute error = 1.568967178400271e-12 relative error = 1.27217888935094e-10 % Correct digits = 12 h = 1e-05 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] = 0.3900000000002553 y[1] (analytic) = 1.245107312665081 y[1] (numeric) = 1.245107312666639 absolute error = 1.558086992758945e-12 relative error = 1.251367634669134e-10 % Correct digits = 12 h = 1e-05 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] = 0.4000000000002653 y[1] (analytic) = 1.257209910215132 y[1] (numeric) = 1.257209910216679 absolute error = 1.547872940932393e-12 relative error = 1.231196897475557e-10 % Correct digits = 12 h = 1e-05 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] = 0.4100000000002753 y[1] (analytic) = 1.269599904832972 y[1] (numeric) = 1.269599904834511 absolute error = 1.538769112130467e-12 relative error = 1.212011048735e-10 % Correct digits = 12 h = 1e-05 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] = 0.4200000000002853 y[1] (analytic) = 1.282278130895457 y[1] (numeric) = 1.282278130896982 absolute error = 1.525002346625115e-12 relative error = 1.189291394652544e-10 % Correct digits = 12 h = 1e-05 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] = 0.4300000000002953 y[1] (analytic) = 1.295245455874892 y[1] (numeric) = 1.295245455876407 absolute error = 1.515898517823189e-12 relative error = 1.170356175308296e-10 % Correct digits = 12 h = 1e-05 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] = 0.4400000000003053 y[1] (analytic) = 1.308502773959522 y[1] (numeric) = 1.308502773961024 absolute error = 1.501909707712912e-12 relative error = 1.14780781332862e-10 % Correct digits = 12 h = 1e-05 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] = 0.4500000000003153 y[1] (analytic) = 1.322050999766038 y[1] (numeric) = 1.322050999767523 absolute error = 1.485256362343534e-12 relative error = 1.12344861325802e-10 % Correct digits = 12 h = 1e-05 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] = 0.4600000000003253 y[1] (analytic) = 1.335891062130784 y[1] (numeric) = 1.335891062132255 absolute error = 1.471267552233257e-12 relative error = 1.10133797129127e-10 % Correct digits = 12 h = 1e-05 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] = 0.4700000000003353 y[1] (analytic) = 1.350023897967471 y[1] (numeric) = 1.350023897968923 absolute error = 1.45194967160478e-12 relative error = 1.075499236562229e-10 % Correct digits = 12 h = 1e-05 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] = 0.4800000000003453 y[1] (analytic) = 1.36445044618031 y[1] (numeric) = 1.364450446181745 absolute error = 1.435740415445252e-12 relative error = 1.052248118987768e-10 % Correct digits = 12 h = 1e-05 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] = 0.4900000000003553 y[1] (analytic) = 1.379171641622462 y[1] (numeric) = 1.379171641623882 absolute error = 1.420863426915275e-12 relative error = 1.03022958421895e-10 % Correct digits = 12 h = 1e-05 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] = 0.5000000000003653 y[1] (analytic) = 1.394188409090671 y[1] (numeric) = 1.394188409092077 absolute error = 1.405986438385298e-12 relative error = 1.008462291909544e-10 % Correct digits = 12 h = 1e-05 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] = 0.5100000000003198 y[1] (analytic) = 1.409501657347733 y[1] (numeric) = 1.409501657349205 absolute error = 1.471711641443108e-12 relative error = 1.044136155336231e-10 % Correct digits = 12 h = 1e-05 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] = 0.5200000000002742 y[1] (analytic) = 1.425112273165809 y[1] (numeric) = 1.425112273167354 absolute error = 1.545208405673293e-12 relative error = 1.084271348137854e-10 % Correct digits = 12 h = 1e-05 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] = 0.5300000000002287 y[1] (analytic) = 1.441021115383106 y[1] (numeric) = 1.44102111538472 absolute error = 1.614708367014828e-12 relative error = 1.120530677710122e-10 % Correct digits = 12 h = 1e-05 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] = 0.5400000000001832 y[1] (analytic) = 1.457229008968903 y[1] (numeric) = 1.457229008970596 absolute error = 1.692868067948439e-12 relative error = 1.161703519164958e-10 % Correct digits = 12 h = 1e-05 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] = 0.5500000000001377 y[1] (analytic) = 1.473736739091337 y[1] (numeric) = 1.473736739093103 absolute error = 1.765920742968774e-12 relative error = 1.198260650038207e-10 % Correct digits = 12 h = 1e-05 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] = 0.5600000000000922 y[1] (analytic) = 1.490545045183564 y[1] (numeric) = 1.490545045185406 absolute error = 1.84163795324821e-12 relative error = 1.23554666073269e-10 % Correct digits = 12 h = 1e-05 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] = 0.5700000000000467 y[1] (analytic) = 1.507654615004472 y[1] (numeric) = 1.507654615006394 absolute error = 1.922018100231071e-12 relative error = 1.274839794938956e-10 % Correct digits = 12 h = 1e-05 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] = 0.5800000000000012 y[1] (analytic) = 1.525066078690767 y[1] (numeric) = 1.525066078692767 absolute error = 1.999955756559757e-12 relative error = 1.311389574854797e-10 % Correct digits = 12 h = 1e-05 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] = 0.5900099999999556 y[1] (analytic) = 1.542797868275412 y[1] (numeric) = 1.542797868277491 absolute error = 2.079447725122918e-12 relative error = 1.347841974559759e-10 % Correct digits = 12 h = 1e-05 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] = 0.6000099999999101 y[1] (analytic) = 1.560815052986506 y[1] (numeric) = 1.560815052988667 absolute error = 2.161382184340255e-12 relative error = 1.384777895500564e-10 % Correct digits = 12 h = 1e-05 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] = 0.6100099999998646 y[1] (analytic) = 1.579135616963 y[1] (numeric) = 1.579135616965246 absolute error = 2.245759134211767e-12 relative error = 1.422144564461677e-10 % Correct digits = 12 h = 1e-05 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] = 0.6200099999998191 y[1] (analytic) = 1.597759900038523 y[1] (numeric) = 1.597759900040853 absolute error = 2.330136084083279e-12 relative error = 1.45837687128529e-10 % Correct digits = 12 h = 1e-05 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] = 0.6300099999997736 y[1] (analytic) = 1.616688154479419 y[1] (numeric) = 1.616688154481835 absolute error = 2.416067346189266e-12 relative error = 1.494454783685385e-10 % Correct digits = 12 h = 1e-05 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] = 0.6400099999997281 y[1] (analytic) = 1.635920538950876 y[1] (numeric) = 1.63592053895338 absolute error = 2.503774965134653e-12 relative error = 1.530499132152431e-10 % Correct digits = 12 h = 1e-05 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] = 0.6500099999996826 y[1] (analytic) = 1.655457112468153 y[1] (numeric) = 1.655457112470744 absolute error = 2.59148258408004e-12 relative error = 1.565418134098533e-10 % Correct digits = 12 h = 1e-05 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] = 0.6600099999996371 y[1] (analytic) = 1.675297828334146 y[1] (numeric) = 1.675297828336828 absolute error = 2.681188604469753e-12 relative error = 1.600425046295098e-10 % Correct digits = 12 h = 1e-05 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] = 0.6700099999995915 y[1] (analytic) = 1.695442528065001 y[1] (numeric) = 1.695442528067773 absolute error = 2.772226892489016e-12 relative error = 1.635105199144051e-10 % Correct digits = 12 h = 1e-05 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] = 0.680009999999546 y[1] (analytic) = 1.715890935305978 y[1] (numeric) = 1.715890935308847 absolute error = 2.868594251026479e-12 relative error = 1.671781225719309e-10 % Correct digits = 12 h = 1e-05 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] = 0.6900099999995005 y[1] (analytic) = 1.736642649740272 y[1] (numeric) = 1.736642649743234 absolute error = 2.962075029699918e-12 relative error = 1.705633009843976e-10 % Correct digits = 12 h = 1e-05 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] = 0.700009999999455 y[1] (analytic) = 1.757697140993933 y[1] (numeric) = 1.757697140996992 absolute error = 3.058886477447231e-12 relative error = 1.740280737850839e-10 % Correct digits = 12 h = 1e-05 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] = 0.7100099999994095 y[1] (analytic) = 1.779053742540517 y[1] (numeric) = 1.779053742543672 absolute error = 3.154365657564995e-12 relative error = 1.773058105069108e-10 % Correct digits = 12 h = 1e-05 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] = 0.720009999999364 y[1] (analytic) = 1.800711645609555 y[1] (numeric) = 1.800711645612807 absolute error = 3.252065283732009e-12 relative error = 1.805988922024858e-10 % Correct digits = 12 h = 1e-05 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] = 0.7300099999993185 y[1] (analytic) = 1.822669893103368 y[1] (numeric) = 1.822669893106723 absolute error = 3.355093980417223e-12 relative error = 1.840757886610326e-10 % Correct digits = 12 h = 1e-05 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] = 0.740009999999273 y[1] (analytic) = 1.844927373527216 y[1] (numeric) = 1.84492737353067 absolute error = 3.454569963423637e-12 relative error = 1.872469351906809e-10 % Correct digits = 12 h = 1e-05 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] = 0.7500099999992275 y[1] (analytic) = 1.867482814938193 y[1] (numeric) = 1.867482814941749 absolute error = 3.555822303269451e-12 relative error = 1.90407230247371e-10 % Correct digits = 12 h = 1e-05 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] = 0.760009999999182 y[1] (analytic) = 1.890334778918718 y[1] (numeric) = 1.890334778922379 absolute error = 3.660849401398991e-12 relative error = 1.936614319445054e-10 % Correct digits = 12 h = 1e-05 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] = 0.7700099999991364 y[1] (analytic) = 1.913481654580894 y[1] (numeric) = 1.913481654584658 absolute error = 3.763434008874356e-12 relative error = 1.966799106677954e-10 % Correct digits = 12 h = 1e-05 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] = 0.7800099999990909 y[1] (analytic) = 1.936921652608426 y[1] (numeric) = 1.9369216526123 absolute error = 3.874456311336871e-12 relative error = 2.00031648472678e-10 % Correct digits = 12 h = 1e-05 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] = 0.7900099999990454 y[1] (analytic) = 1.960652799343187 y[1] (numeric) = 1.960652799347169 absolute error = 3.981925900120586e-12 relative error = 2.030918427502575e-10 % Correct digits = 12 h = 1e-05 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] = 0.8000099999989999 y[1] (analytic) = 1.984672930923937 y[1] (numeric) = 1.984672930928027 absolute error = 4.090061622719077e-12 relative error = 2.060824007316412e-10 % Correct digits = 12 h = 1e-05 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] = 0.8100099999989544 y[1] (analytic) = 2.008979687485067 y[1] (numeric) = 2.008979687489266 absolute error = 4.199307568342192e-12 relative error = 2.090268803861864e-10 % Correct digits = 12 h = 1e-05 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] = 0.8200099999989089 y[1] (analytic) = 2.033570507423635 y[1] (numeric) = 2.033570507427938 absolute error = 4.302780354237257e-12 relative error = 2.115874683729812e-10 % Correct digits = 12 h = 1e-05 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] = 0.8300099999988634 y[1] (analytic) = 2.058442621743335 y[1] (numeric) = 2.058442621747748 absolute error = 4.412914478280072e-12 relative error = 2.143812235360094e-10 % Correct digits = 12 h = 1e-05 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] = 0.8400099999988179 y[1] (analytic) = 2.08359304848438 y[1] (numeric) = 2.083593048488905 absolute error = 4.525713137581988e-12 relative error = 2.172071528494503e-10 % Correct digits = 12 h = 1e-05 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] = 0.8500099999987724 y[1] (analytic) = 2.10901858724863 y[1] (numeric) = 2.109018587253269 absolute error = 4.639399975303604e-12 relative error = 2.199790937526086e-10 % Correct digits = 12 h = 1e-05 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] = 0.8600099999987268 y[1] (analytic) = 2.13471581382965 y[1] (numeric) = 2.134715813834404 absolute error = 4.75441908065477e-12 relative error = 2.227190640484089e-10 % Correct digits = 12 h = 1e-05 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] = 0.8700099999986813 y[1] (analytic) = 2.160681074957659 y[1] (numeric) = 2.160681074962532 absolute error = 4.872546810474887e-12 relative error = 2.255097648120221e-10 % Correct digits = 12 h = 1e-05 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] = 0.8800099999986358 y[1] (analytic) = 2.186910483169678 y[1] (numeric) = 2.186910483174676 absolute error = 4.998668146072305e-12 relative error = 2.285721425061397e-10 % Correct digits = 12 h = 1e-05 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] = 0.8900099999985903 y[1] (analytic) = 2.213399911815431 y[1] (numeric) = 2.213399911820551 absolute error = 5.119904500361372e-12 relative error = 2.313140283882105e-10 % Correct digits = 12 h = 1e-05 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] = 0.9000099999985448 y[1] (analytic) = 2.240144990209862 y[1] (numeric) = 2.240144990215109 absolute error = 5.24646992516864e-12 relative error = 2.342022479838297e-10 % Correct digits = 12 h = 1e-05 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] = 0.9100099999984993 y[1] (analytic) = 2.267141098943345 y[1] (numeric) = 2.267141098948712 absolute error = 5.367262190247857e-12 relative error = 2.367414270223145e-10 % Correct digits = 12 h = 1e-05 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] = 0.9200099999984538 y[1] (analytic) = 2.294383365360908 y[1] (numeric) = 2.29438336536639 absolute error = 5.481837206389173e-12 relative error = 2.389242046098463e-10 % Correct digits = 12 h = 1e-05 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] = 0.9300099999984083 y[1] (analytic) = 2.321866659222033 y[1] (numeric) = 2.321866659227648 absolute error = 5.614175790924492e-12 relative error = 2.417957882562292e-10 % Correct digits = 12 h = 1e-05 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] = 0.9400099999983628 y[1] (analytic) = 2.349585588552716 y[1] (numeric) = 2.349585588558455 absolute error = 5.738520769682509e-12 relative error = 2.442354429496347e-10 % Correct digits = 12 h = 1e-05 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] = 0.9500099999983173 y[1] (analytic) = 2.377534495701708 y[1] (numeric) = 2.377534495707571 absolute error = 5.863309837650377e-12 relative error = 2.466130290959196e-10 % Correct digits = 12 h = 1e-05 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] = 0.9600099999982717 y[1] (analytic) = 2.405707453612957 y[1] (numeric) = 2.405707453618941 absolute error = 5.983213924309894e-12 relative error = 2.487091236020464e-10 % Correct digits = 12 h = 1e-05 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] = 0.9700099999982262 y[1] (analytic) = 2.434098262326394 y[1] (numeric) = 2.434098262332498 absolute error = 6.103118010969411e-12 relative error = 2.507342495342132e-10 % Correct digits = 12 h = 1e-05 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] = 0.9800099999981807 y[1] (analytic) = 2.462700445719309 y[1] (numeric) = 2.462700445725546 absolute error = 6.236344773924429e-12 relative error = 2.532319667527777e-10 % Correct digits = 12 h = 1e-05 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] = 0.9900099999981352 y[1] (analytic) = 2.491507248500616 y[1] (numeric) = 2.491507248506983 absolute error = 6.367795180040048e-12 relative error = 2.555800383030061e-10 % Correct digits = 12 h = 1e-05 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 = 90001 Total Elapsed Time = 3.0 Seconds Elapsed Time(since restart) = 3.0 Seconds Time to Timeout = 9 Minutes 57.0 Seconds Percent Done = 100 %