##############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=10000000; glob_max_minutes=3; 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 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 Radius of convergence (ratio test) for eq 1 = 0.6055 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.675 Order of pole (six term test) = 0.02195 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 Radius of convergence (ratio test) for eq 1 = 0.6247 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6913 Order of pole (six term test) = 0.2368 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 Radius of convergence (ratio test) for eq 1 = 0.635 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7032 Order of pole (six term test) = 0.2358 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 Radius of convergence (ratio test) for eq 1 = 0.6452 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.715 Order of pole (six term test) = 0.2348 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 Radius of convergence (ratio test) for eq 1 = 0.6554 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7268 Order of pole (six term test) = 0.2338 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 Radius of convergence (ratio test) for eq 1 = 0.6657 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7386 Order of pole (six term test) = 0.2328 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 Radius of convergence (ratio test) for eq 1 = 0.6759 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7503 Order of pole (six term test) = 0.2318 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 Radius of convergence (ratio test) for eq 1 = 0.6862 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7619 Order of pole (six term test) = 0.2308 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 Radius of convergence (ratio test) for eq 1 = 0.6964 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7733 Order of pole (six term test) = 0.2299 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 Radius of convergence (ratio test) for eq 1 = 0.7067 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7845 Order of pole (six term test) = 0.2291 TOP MAIN SOLVE Loop x[1] = 0.2000000000000653 y[1] (analytic) = 1.069131582795966 y[1] (numeric) = 1.0691315827977 absolute error = 1.733946319859569e-12 relative error = 1.621826861876998e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7169 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7955 Order of pole (six term test) = 0.2284 TOP MAIN SOLVE Loop x[1] = 0.2100000000000753 y[1] (analytic) = 1.075835852148637 y[1] (numeric) = 1.075835852150367 absolute error = 1.730171561575844e-12 relative error = 1.608211474009145e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7271 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8062 Order of pole (six term test) = 0.228 TOP MAIN SOLVE Loop x[1] = 0.2200000000000853 y[1] (analytic) = 1.082827774695279 y[1] (numeric) = 1.082827774697001 absolute error = 1.722400000403468e-12 relative error = 1.590650000539719e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7374 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8166 Order of pole (six term test) = 0.2278 TOP MAIN SOLVE Loop x[1] = 0.2300000000000953 y[1] (analytic) = 1.090106067817488 y[1] (numeric) = 1.090106067819203 absolute error = 1.714406394626167e-12 relative error = 1.572696864313943e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7476 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8267 Order of pole (six term test) = 0.2279 TOP MAIN SOLVE Loop x[1] = 0.2400000000001053 y[1] (analytic) = 1.097669651455029 y[1] (numeric) = 1.097669651456737 absolute error = 1.707300967268566e-12 relative error = 1.55538687346e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7579 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8363 Order of pole (six term test) = 0.2282 TOP MAIN SOLVE Loop x[1] = 0.2500000000001153 y[1] (analytic) = 1.105517634822656 y[1] (numeric) = 1.105517634824356 absolute error = 1.70041758451589e-12 relative error = 1.538118914574046e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7681 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8458 Order of pole (six term test) = 0.2288 TOP MAIN SOLVE Loop x[1] = 0.2600000000001253 y[1] (analytic) = 1.113649303916657 y[1] (numeric) = 1.113649303918348 absolute error = 1.691313755713963e-12 relative error = 1.518713072208356e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7784 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8551 Order of pole (six term test) = 0.2295 TOP MAIN SOLVE Loop x[1] = 0.2700000000001353 y[1] (analytic) = 1.122064109735975 y[1] (numeric) = 1.122064109737654 absolute error = 1.679545391652937e-12 relative error = 1.496835499041261e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7886 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.865 Order of pole (six term test) = 0.2298 TOP MAIN SOLVE Loop x[1] = 0.2800000000001453 y[1] (analytic) = 1.130761657149848 y[1] (numeric) = 1.130761657151516 absolute error = 1.668443161406685e-12 relative error = 1.47550383483297e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7988 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.876 Order of pole (six term test) = 0.2288 TOP MAIN SOLVE Loop x[1] = 0.2900000000001553 y[1] (analytic) = 1.13974169435028 y[1] (numeric) = 1.139741694351941 absolute error = 1.661559778654009e-12 relative error = 1.457838900595101e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8091 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8899 Order of pole (six term test) = 0.2253 TOP MAIN SOLVE Loop x[1] = 0.3000000000001653 y[1] (analytic) = 1.149004102833311 y[1] (numeric) = 1.149004102834962 absolute error = 1.650679593012683e-12 relative error = 1.436617666501189e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8193 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9089 Order of pole (six term test) = 0.2165 TOP MAIN SOLVE Loop x[1] = 0.3100000000001753 y[1] (analytic) = 1.158548887858167 y[1] (numeric) = 1.15854888785981 absolute error = 1.643574165655082e-12 relative error = 1.418648952046893e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8296 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9374 Order of pole (six term test) = 0.1979 TOP MAIN SOLVE Loop x[1] = 0.3200000000001853 y[1] (analytic) = 1.168376169337918 y[1] (numeric) = 1.168376169339554 absolute error = 1.636024649087631e-12 relative error = 1.400255065125741e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8398 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9826 Order of pole (six term test) = 0.1609 TOP MAIN SOLVE Loop x[1] = 0.3300000000001953 y[1] (analytic) = 1.178486173119407 y[1] (numeric) = 1.178486173121033 absolute error = 1.626032641866004e-12 relative error = 1.379763869067686e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.057 Order of pole (six term test) = 0.08802 TOP MAIN SOLVE Loop x[1] = 0.3400000000002053 y[1] (analytic) = 1.188879222613892 y[1] (numeric) = 1.188879222615508 absolute error = 1.616040634644378e-12 relative error = 1.359297566906183e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8603 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.187 Order of pole (six term test) = -0.05977 TOP MAIN SOLVE Loop x[1] = 0.3500000000002153 y[1] (analytic) = 1.199555730743213 y[1] (numeric) = 1.199555730744818 absolute error = 1.605160449003051e-12 relative error = 1.338129115525576e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8705 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.427 Order of pole (six term test) = -0.3924 TOP MAIN SOLVE Loop x[1] = 0.3600000000002253 y[1] (analytic) = 1.210516192169308 y[1] (numeric) = 1.210516192170898 absolute error = 1.589395282053374e-12 relative error = 1.312989691781896e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8808 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.964 Order of pole (six term test) = -1.376 TOP MAIN SOLVE Loop x[1] = 0.3700000000002353 y[1] (analytic) = 1.221761175777635 y[1] (numeric) = 1.221761175779216 absolute error = 1.580957587066223e-12 relative error = 1.293998875074717e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.891 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.71 Order of pole (six term test) = -11.36 TOP MAIN SOLVE Loop x[1] = 0.3800000000002453 y[1] (analytic) = 1.233291317387566 y[1] (numeric) = 1.233291317389135 absolute error = 1.569189223005196e-12 relative error = 1.272358931650593e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9013 Order of pole (ratio test) Not computed 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 = 1.55830903736387e-12 relative error = 1.251545968377937e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9115 Order of pole (ratio test) Not computed 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) = 1.25720991021668 absolute error = 1.548094985537318e-12 relative error = 1.2313735144455e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9217 Order of pole (ratio test) Not computed 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 = 1.538991156735392e-12 relative error = 1.212185942104226e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.932 Order of pole (ratio test) Not computed 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 = 1.52522439123004e-12 relative error = 1.189464558804357e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9422 Order of pole (ratio test) Not computed 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) = 1.295245455876408 absolute error = 1.516120562428114e-12 relative error = 1.170527605830533e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9525 Order of pole (ratio test) Not computed 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 = 1.502131752317837e-12 relative error = 1.147977506973405e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9627 Order of pole (ratio test) Not computed 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 = 1.485034317738609e-12 relative error = 1.123280658614089e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9729 Order of pole (ratio test) Not computed 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 = 1.471045507628332e-12 relative error = 1.101171756686487e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9832 Order of pole (ratio test) Not computed 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 Radius of convergence (ratio test) for eq 1 = 0.9934 Order of pole (ratio test) Not computed 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 Radius of convergence (ratio test) for eq 1 = 1.004 Order of pole (ratio test) Not computed 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 Radius of convergence (ratio test) for eq 1 = 1.014 Order of pole (ratio test) Not computed 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 Radius of convergence (ratio test) for eq 1 = 1.024 Order of pole (ratio test) Not computed 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 Radius of convergence (ratio test) for eq 1 = 1.034 Order of pole (ratio test) Not computed 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 = 1.545430450278218e-12 relative error = 1.084427156637371e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.045 Order of pole (ratio test) Not computed 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) = 1.441021115384721 absolute error = 1.614930411619753e-12 relative error = 1.120684766087145e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.055 Order of pole (ratio test) Not computed 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 Radius of convergence (ratio test) for eq 1 = 1.065 Order of pole (ratio test) Not computed 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 Radius of convergence (ratio test) for eq 1 = 1.075 Order of pole (ratio test) Not computed 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) = 1.490545045185407 absolute error = 1.84208204245806e-12 relative error = 1.235844598196093e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.086 Order of pole (ratio test) Not computed 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) = 1.507654615006395 absolute error = 1.922684234045846e-12 relative error = 1.275281629433505e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.096 Order of pole (ratio test) Not computed 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) = 1.525066078692768 absolute error = 2.000843934979457e-12 relative error = 1.311971961698299e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.106 Order of pole (ratio test) Not computed 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) = 1.542797868277492 absolute error = 2.080335903542618e-12 relative error = 1.348417667875108e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.116 Order of pole (ratio test) Not computed 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) = 1.560815052988668 absolute error = 2.162270362759955e-12 relative error = 1.385346943331055e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.126 Order of pole (ratio test) Not computed 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) = 1.579135616965247 absolute error = 2.246647312631467e-12 relative error = 1.422707010403722e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.137 Order of pole (ratio test) Not computed 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) = 1.597759900040854 absolute error = 2.331024262502979e-12 relative error = 1.458932761078042e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.147 Order of pole (ratio test) Not computed 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) = 1.616688154481836 absolute error = 2.416955524608966e-12 relative error = 1.495004165096537e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.157 Order of pole (ratio test) Not computed 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 = 2.504441098949428e-12 relative error = 1.5309063241883e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.167 Order of pole (ratio test) Not computed 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) = 1.655457112470745 absolute error = 2.59192667328989e-12 relative error = 1.565686391854354e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.176 Order of pole (ratio test) Not computed 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 = 2.681632693679603e-12 relative error = 1.600690127048107e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.185 Order of pole (ratio test) Not computed 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) = 1.695442528067774 absolute error = 2.772670981698866e-12 relative error = 1.635367130293293e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.194 Order of pole (ratio test) Not computed 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 = 2.86903834023633e-12 relative error = 1.672040035414443e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.202 Order of pole (ratio test) Not computed 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) = 1.736642649743235 absolute error = 2.962519118909768e-12 relative error = 1.705888726936906e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.211 Order of pole (ratio test) Not computed 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) = 1.757697140996993 absolute error = 3.059330566657081e-12 relative error = 1.740533391848784e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.219 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.07147 Order of pole (six term test) = -12.53 TOP MAIN SOLVE Loop x[1] = 0.7100099999994095 y[1] (analytic) = 1.779053742540517 y[1] (numeric) = 1.779053742543672 absolute error = 3.15458770216992e-12 relative error = 1.773182915579109e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.227 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.124 Order of pole (six term test) = -12.37 TOP MAIN SOLVE Loop x[1] = 0.720009999999364 y[1] (analytic) = 1.800711645609555 y[1] (numeric) = 1.800711645612807 absolute error = 3.252287328336934e-12 relative error = 1.80611223138728e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.234 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1526 Order of pole (six term test) = -12.25 TOP MAIN SOLVE Loop x[1] = 0.7300099999993185 y[1] (analytic) = 1.822669893103368 y[1] (numeric) = 1.822669893106723 absolute error = 3.355316025022148e-12 relative error = 1.840879710428103e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.242 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1725 Order of pole (six term test) = -12.14 TOP MAIN SOLVE Loop x[1] = 0.740009999999273 y[1] (analytic) = 1.844927373527216 y[1] (numeric) = 1.844927373530671 absolute error = 3.455014052633487e-12 relative error = 1.87271006014076e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.249 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1877 Order of pole (six term test) = -12.05 TOP MAIN SOLVE Loop x[1] = 0.7500099999992275 y[1] (analytic) = 1.867482814938193 y[1] (numeric) = 1.867482814941749 absolute error = 3.556044347874376e-12 relative error = 1.904191202954694e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.257 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1992 Order of pole (six term test) = -11.97 TOP MAIN SOLVE Loop x[1] = 0.760009999999182 y[1] (analytic) = 1.890334778918718 y[1] (numeric) = 1.890334778922379 absolute error = 3.661071446003916e-12 relative error = 1.936731782556563e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.264 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2075 Order of pole (six term test) = -11.9 TOP MAIN SOLVE Loop x[1] = 0.7700099999991364 y[1] (analytic) = 1.913481654580894 y[1] (numeric) = 1.913481654584658 absolute error = 3.763656053479281e-12 relative error = 1.966915148869627e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.273 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.212 Order of pole (six term test) = -11.82 TOP MAIN SOLVE Loop x[1] = 0.7800099999990909 y[1] (analytic) = 1.936921652608426 y[1] (numeric) = 1.9369216526123 absolute error = 3.874678355941796e-12 relative error = 2.000431122613463e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.281 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2125 Order of pole (six term test) = -11.75 TOP MAIN SOLVE Loop x[1] = 0.7900099999990454 y[1] (analytic) = 1.960652799343187 y[1] (numeric) = 1.960652799347169 absolute error = 3.982147944725511e-12 relative error = 2.031031677847052e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.281 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2082 Order of pole (six term test) = -11.68 TOP MAIN SOLVE Loop x[1] = 0.8000099999989999 y[1] (analytic) = 1.984672930923937 y[1] (numeric) = 1.984672930928028 absolute error = 4.090283667324002e-12 relative error = 2.060935887012792e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.278 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1982 Order of pole (six term test) = -11.61 TOP MAIN SOLVE Loop x[1] = 0.8100099999989544 y[1] (analytic) = 2.008979687485067 y[1] (numeric) = 2.008979687489266 absolute error = 4.199751657552042e-12 relative error = 2.090489855977332e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.272 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1814 Order of pole (six term test) = -11.54 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 Radius of convergence (ratio test) for eq 1 = 1.262 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1553 Order of pole (six term test) = -11.47 TOP MAIN SOLVE Loop x[1] = 0.8300099999988634 y[1] (analytic) = 2.058442621743335 y[1] (numeric) = 2.058442621747749 absolute error = 4.413358567489922e-12 relative error = 2.144027975748074e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.248 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1142 Order of pole (six term test) = -11.41 TOP MAIN SOLVE Loop x[1] = 0.8400099999988179 y[1] (analytic) = 2.08359304848438 y[1] (numeric) = 2.083593048488906 absolute error = 4.526157226791838e-12 relative error = 2.172284664744969e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.229 Order of pole (ratio test) Not computed 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) = 2.10901858725327 absolute error = 4.640288153723304e-12 relative error = 2.200212071045283e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.206 Order of pole (ratio test) Not computed 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) = 2.134715813834405 absolute error = 4.75530725907447e-12 relative error = 2.227606704493146e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.176 Order of pole (ratio test) Not computed 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 = 4.873434988894587e-12 relative error = 2.255508712219404e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.14 Order of pole (ratio test) Not computed 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) = 2.186910483174677 absolute error = 4.999556324492005e-12 relative error = 2.286127558932233e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.097 Order of pole (ratio test) Not computed 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 = 5.120792678781072e-12 relative error = 2.313541557242133e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.047 Order of pole (ratio test) Not computed 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 = 5.24691401437849e-12 relative error = 2.342220721118121e-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 = 5.367706279457707e-12 relative error = 2.367610150933903e-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) = 2.294383365366391 absolute error = 5.482281295599023e-12 relative error = 2.389435601027667e-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 = 5.615063969344192e-12 relative error = 2.418340410308308e-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) = 2.349585588558456 absolute error = 5.739408948102209e-12 relative error = 2.442732444421204e-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) = 2.377534495707572 absolute error = 5.864198016070077e-12 relative error = 2.46650386216134e-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) = 2.405707453618942 absolute error = 5.984546191939444e-12 relative error = 2.487645030550863e-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) = 2.434098262332499 absolute error = 6.104450278598961e-12 relative error = 2.507889830529939e-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) = 2.462700445725547 absolute error = 6.23812113076383e-12 relative error = 2.533040971997627e-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) = 2.491507248506985 absolute error = 6.369571536879448e-12 relative error = 2.556513347778797e-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 = 7 Seconds Elapsed Time(since restart) = 7 Seconds Time to Timeout = 2 Minutes 53 Seconds Percent Done = 100 %