##############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; 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 = 7.512525334680391e-129 estimated_step_error = 7.512525334680391e-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 = 5.041537794430858e-121 estimated_step_error = 5.041537794430858e-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 Radius of convergence (three term test) for eq 1 = 0.601 Order of pole (three term test) = 0.8273 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 Radius of convergence (three term test) for eq 1 = 0.6099 Order of pole (three term test) = 0.4554 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 Radius of convergence (three term test) for eq 1 = 0.6199 Order of pole (three term test) = 0.4557 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 Radius of convergence (three term test) for eq 1 = 0.6299 Order of pole (three term test) = 0.4559 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 Radius of convergence (three term test) for eq 1 = 0.6399 Order of pole (three term test) = 0.4562 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 Radius of convergence (three term test) for eq 1 = 0.65 Order of pole (three term test) = 0.4564 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 Radius of convergence (three term test) for eq 1 = 0.66 Order of pole (three term test) = 0.4567 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 Radius of convergence (three term test) for eq 1 = 0.67 Order of pole (three term test) = 0.457 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 Radius of convergence (three term test) for eq 1 = 0.68 Order of pole (three term test) = 0.4573 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 Radius of convergence (three term test) for eq 1 = 0.69 Order of pole (three term test) = 0.4576 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 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0.4579 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 Radius of convergence (three term test) for eq 1 = 0.71 Order of pole (three term test) = 0.4582 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 Radius of convergence (three term test) for eq 1 = 0.72 Order of pole (three term test) = 0.4585 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 Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 0.4588 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 Radius of convergence (three term test) for eq 1 = 0.74 Order of pole (three term test) = 0.4591 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 Radius of convergence (three term test) for eq 1 = 0.7501 Order of pole (three term test) = 0.4595 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 Radius of convergence (three term test) for eq 1 = 0.7601 Order of pole (three term test) = 0.4598 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 Radius of convergence (three term test) for eq 1 = 0.7701 Order of pole (three term test) = 0.4601 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 Radius of convergence (three term test) for eq 1 = 0.7801 Order of pole (three term test) = 0.4605 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 Radius of convergence (three term test) for eq 1 = 0.7901 Order of pole (three term test) = 0.4608 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 Radius of convergence (three term test) for eq 1 = 0.8001 Order of pole (three term test) = 0.4612 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 Radius of convergence (three term test) for eq 1 = 0.8101 Order of pole (three term test) = 0.4615 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 Radius of convergence (three term test) for eq 1 = 0.8202 Order of pole (three term test) = 0.4619 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 Radius of convergence (three term test) for eq 1 = 0.8302 Order of pole (three term test) = 0.4622 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 Radius of convergence (three term test) for eq 1 = 0.8402 Order of pole (three term test) = 0.4626 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 Radius of convergence (three term test) for eq 1 = 0.8502 Order of pole (three term test) = 0.463 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 Radius of convergence (three term test) for eq 1 = 0.8602 Order of pole (three term test) = 0.4633 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 Radius of convergence (three term test) for eq 1 = 0.8702 Order of pole (three term test) = 0.4637 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 Radius of convergence (three term test) for eq 1 = 0.8803 Order of pole (three term test) = 0.4641 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 Radius of convergence (three term test) for eq 1 = 0.8903 Order of pole (three term test) = 0.4645 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 Radius of convergence (three term test) for eq 1 = 0.9003 Order of pole (three term test) = 0.4649 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 Radius of convergence (three term test) for eq 1 = 0.9103 Order of pole (three term test) = 0.4653 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 Radius of convergence (three term test) for eq 1 = 0.9203 Order of pole (three term test) = 0.4658 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 Radius of convergence (three term test) for eq 1 = 0.9304 Order of pole (three term test) = 0.4663 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 Radius of convergence (three term test) for eq 1 = 0.9404 Order of pole (three term test) = 0.4669 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 Radius of convergence (three term test) for eq 1 = 0.9504 Order of pole (three term test) = 0.4677 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 Radius of convergence (three term test) for eq 1 = 0.9605 Order of pole (three term test) = 0.4686 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 Radius of convergence (three term test) for eq 1 = 0.9705 Order of pole (three term test) = 0.4697 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 Radius of convergence (three term test) for eq 1 = 0.9806 Order of pole (three term test) = 0.4712 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 Radius of convergence (three term test) for eq 1 = 0.9907 Order of pole (three term test) = 0.4731 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 Radius of convergence (three term test) for eq 1 = 1.001 Order of pole (three term test) = 0.4755 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 Radius of convergence (three term test) for eq 1 = 1.011 Order of pole (three term test) = 0.4786 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 Radius of convergence (three term test) for eq 1 = 1.021 Order of pole (three term test) = 0.4827 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 Radius of convergence (three term test) for eq 1 = 1.031 Order of pole (three term test) = 0.4879 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 Finished! Maximum Iterations Reached before Solution Completed! 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 = 50000 Total Elapsed Time = 2.0 Seconds Elapsed Time(since restart) = 2.0 Seconds Expected Time Remaining = 1.6 Seconds Optimized Time Remaining = 1.6 Seconds Expected Total Time = 3.6 Seconds Time to Timeout = 9 Minutes 58.0 Seconds Percent Done = 55.56 %