##############ECHO OF PROBLEM################# ##############temp/exp_sqrtpostode.ode################# diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=2.0; x_end=3.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_display_interval=0.01; glob_max_minutes=10; 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=30.0; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(20.0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x + 0.2))); } // 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 = 1 estimated_steps = 1000000 step_error = 1e-16 est_needed_step_err = 1e-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 = 6.901394628596011e-176 estimated_step_error = 6.901394628596011e-176 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 = 4.631447010427056e-168 estimated_step_error = 4.631447010427056e-168 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 = 3.108110770842568e-160 estimated_step_error = 3.108110770842568e-160 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 = 2.085816884453821e-152 estimated_step_error = 2.085816884453821e-152 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 = 1.399766746954624e-144 estimated_step_error = 1.399766746954624e-144 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = -13.83604079041925 y[1] (numeric) = -13.83604079041925 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 = 3.996 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 27.58 Order of pole (six term test) = 2.738 TOP MAIN SOLVE Loop x[1] = 2.010000000000066 y[1] (analytic) = -13.81721108362767 y[1] (numeric) = -13.81721109106627 absolute error = 7.438602622755752e-09 relative error = 5.383577465621788e-08 % Correct digits = 10 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 = 4.006 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 27.65 Order of pole (six term test) = 2.741 TOP MAIN SOLVE Loop x[1] = 2.020000000000131 y[1] (analytic) = -13.79836650334301 y[1] (numeric) = -13.7983665182168 absolute error = 1.487378575859566e-08 relative error = 1.077938157026928e-07 % Correct digits = 9 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 = 4.016 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 27.72 Order of pole (six term test) = 2.745 TOP MAIN SOLVE Loop x[1] = 2.030000000000197 y[1] (analytic) = -13.77950705634961 y[1] (numeric) = -13.77950707865521 absolute error = 2.230559381644071e-08 relative error = 1.618751216950266e-07 % Correct digits = 9 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 = 4.026 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 27.79 Order of pole (six term test) = 2.748 TOP MAIN SOLVE Loop x[1] = 2.040000000000262 y[1] (analytic) = -13.76063274939731 y[1] (numeric) = -13.76063277913134 absolute error = 2.973402324357721e-08 relative error = 2.160803488115726e-07 % Correct digits = 9 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 = 4.036 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 27.86 Order of pole (six term test) = 2.751 TOP MAIN SOLVE Loop x[1] = 2.050000000000328 y[1] (analytic) = -13.7417435892017 y[1] (numeric) = -13.74174362636084 absolute error = 3.715914154156508e-08 relative error = 2.704106746014737e-07 % Correct digits = 9 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 = 4.046 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 27.93 Order of pole (six term test) = 2.754 TOP MAIN SOLVE Loop x[1] = 2.060000000000393 y[1] (analytic) = -13.72283958244425 y[1] (numeric) = -13.72283962702515 absolute error = 4.458089719605596e-08 relative error = 3.248664165184055e-07 % Correct digits = 9 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 = 4.056 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 28 Order of pole (six term test) = 2.757 TOP MAIN SOLVE Loop x[1] = 2.070000000000459 y[1] (analytic) = -13.70392073577263 y[1] (numeric) = -13.70392078777197 absolute error = 5.199933816868452e-08 relative error = 3.794486203714369e-07 % Correct digits = 9 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 = 4.066 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 28.07 Order of pole (six term test) = 2.761 TOP MAIN SOLVE Loop x[1] = 2.080000000000524 y[1] (analytic) = -13.68498705580087 y[1] (numeric) = -13.68498711521533 absolute error = 5.941446090673708e-08 relative error = 4.341579620387886e-07 % Correct digits = 9 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 = 4.076 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 28.14 Order of pole (six term test) = 2.764 TOP MAIN SOLVE Loop x[1] = 2.09000000000059 y[1] (analytic) = -13.66603854910955 y[1] (numeric) = -13.66603861593584 absolute error = 6.682629205556623e-08 relative error = 4.889953428378152e-07 % Correct digits = 9 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 = 4.086 Order of pole (three term test) = 1.539 Radius of convergence (six term test) for eq 1 = 28.21 Order of pole (six term test) = 2.767 TOP MAIN SOLVE Loop x[1] = 2.100000000000655 y[1] (analytic) = -13.64707522224605 y[1] (numeric) = -13.64707529648096 absolute error = 7.423491155122974e-08 relative error = 5.439620603117924e-07 % Correct digits = 9 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 = 4.096 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.28 Order of pole (six term test) = 2.77 TOP MAIN SOLVE Loop x[1] = 2.110000000000721 y[1] (analytic) = -13.62809708172475 y[1] (numeric) = -13.62809716336503 absolute error = 8.164028031387716e-08 relative error = 5.990585466503363e-07 % Correct digits = 9 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 = 4.106 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.35 Order of pole (six term test) = 2.774 TOP MAIN SOLVE Loop x[1] = 2.120000000000786 y[1] (analytic) = -13.60910413402718 y[1] (numeric) = -13.60910422306959 absolute error = 8.904240189622215e-08 relative error = 6.542855504616736e-07 % Correct digits = 9 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 = 4.116 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.41 Order of pole (six term test) = 2.777 TOP MAIN SOLVE Loop x[1] = 2.130000000000852 y[1] (analytic) = -13.59009638560233 y[1] (numeric) = -13.59009648204361 absolute error = 9.644128162733523e-08 relative error = 7.096438383579635e-07 % Correct digits = 9 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 = 4.126 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.48 Order of pole (six term test) = 2.78 TOP MAIN SOLVE Loop x[1] = 2.140000000000917 y[1] (analytic) = -13.57107384286673 y[1] (numeric) = -13.57107394670372 absolute error = 1.038369887851331e-07 relative error = 7.651346532147289e-07 % Correct digits = 9 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 = 4.136 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.55 Order of pole (six term test) = 2.784 TOP MAIN SOLVE Loop x[1] = 2.150000000000983 y[1] (analytic) = -13.55203651220475 y[1] (numeric) = -13.55203662343422 absolute error = 1.11229466526197e-07 relative error = 8.207583150032505e-07 % Correct digits = 9 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 = 4.146 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.62 Order of pole (six term test) = 2.787 TOP MAIN SOLVE Loop x[1] = 2.160000000001048 y[1] (analytic) = -13.53298439996874 y[1] (numeric) = -13.53298451858753 absolute error = 1.186187983392983e-07 relative error = 8.765161832269043e-07 % Correct digits = 9 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 = 4.156 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.69 Order of pole (six term test) = 2.79 TOP MAIN SOLVE Loop x[1] = 2.170000000001114 y[1] (analytic) = -13.51391751247923 y[1] (numeric) = -13.5139176384842 absolute error = 1.260049664608687e-07 relative error = 9.324088765860174e-07 % Correct digits = 9 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 = 4.166 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.76 Order of pole (six term test) = 2.794 TOP MAIN SOLVE Loop x[1] = 2.180000000001179 y[1] (analytic) = -13.49483585602516 y[1] (numeric) = -13.49483598941318 absolute error = 1.333880206288995e-07 relative error = 9.884375182625477e-07 % Correct digits = 9 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 = 4.176 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.83 Order of pole (six term test) = 2.797 TOP MAIN SOLVE Loop x[1] = 2.190000000001245 y[1] (analytic) = -13.47573943686404 y[1] (numeric) = -13.47573957763197 absolute error = 1.407679341980383e-07 relative error = 1.044602671768464e-06 % Correct digits = 8 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 = 4.186 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.9 Order of pole (six term test) = 2.8 TOP MAIN SOLVE Loop x[1] = 2.20000000000131 y[1] (analytic) = -13.45662826122215 y[1] (numeric) = -13.45662840936689 absolute error = 1.48144740919065e-07 relative error = 1.100905353430714e-06 % Correct digits = 8 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 = 4.196 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 28.97 Order of pole (six term test) = 2.804 TOP MAIN SOLVE Loop x[1] = 2.210000000001376 y[1] (analytic) = -13.43750233529473 y[1] (numeric) = -13.4375024908132 absolute error = 1.555184709900459e-07 relative error = 1.15734655972162e-06 % Correct digits = 8 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 = 4.206 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.04 Order of pole (six term test) = 2.807 TOP MAIN SOLVE Loop x[1] = 2.220000000001441 y[1] (analytic) = -13.41836166524617 y[1] (numeric) = -13.41836182813532 absolute error = 1.628891475036198e-07 relative error = 1.213927240651935e-06 % Correct digits = 8 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 = 4.216 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.11 Order of pole (six term test) = 2.81 TOP MAIN SOLVE Loop x[1] = 2.230000000001507 y[1] (analytic) = -13.39920625721021 y[1] (numeric) = -13.39920642746693 absolute error = 1.702567260508658e-07 relative error = 1.270647848705587e-06 % Correct digits = 8 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 = 4.226 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.18 Order of pole (six term test) = 2.814 TOP MAIN SOLVE Loop x[1] = 2.240000000001572 y[1] (analytic) = -13.38003611729008 y[1] (numeric) = -13.38003629491136 absolute error = 1.776212812387712e-07 relative error = 1.327509729284241e-06 % Correct digits = 8 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 = 4.236 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.26 Order of pole (six term test) = 2.817 TOP MAIN SOLVE Loop x[1] = 2.250000000001638 y[1] (analytic) = -13.36085125155874 y[1] (numeric) = -13.36085143654151 absolute error = 1.849827686584149e-07 relative error = 1.384513345561226e-06 % Correct digits = 8 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 = 4.246 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.33 Order of pole (six term test) = 2.821 TOP MAIN SOLVE Loop x[1] = 2.260000000001703 y[1] (analytic) = -13.34165166605904 y[1] (numeric) = -13.34165185840032 absolute error = 1.923412771276389e-07 relative error = 1.441660162788931e-06 % Correct digits = 8 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 = 4.256 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.4 Order of pole (six term test) = 2.824 TOP MAIN SOLVE Loop x[1] = 2.270000000001769 y[1] (analytic) = -13.32243736680387 y[1] (numeric) = -13.32243756650064 absolute error = 1.99696776448377e-07 relative error = 1.498950762162866e-06 % Correct digits = 8 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 = 4.266 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.47 Order of pole (six term test) = 2.827 TOP MAIN SOLVE Loop x[1] = 2.280000000001834 y[1] (analytic) = -13.30320835977638 y[1] (numeric) = -13.30320856682568 absolute error = 2.070493003714091e-07 relative error = 1.556386209791647e-06 % Correct digits = 8 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 = 4.276 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.54 Order of pole (six term test) = 2.831 TOP MAIN SOLVE Loop x[1] = 2.2900000000019 y[1] (analytic) = -13.28396465093016 y[1] (numeric) = -13.28396486532901 absolute error = 2.143988542258057e-07 relative error = 1.613967364861915e-06 % Correct digits = 8 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 = 4.286 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.61 Order of pole (six term test) = 2.834 TOP MAIN SOLVE Loop x[1] = 2.300000000001965 y[1] (analytic) = -13.26470624618935 y[1] (numeric) = -13.2647064679348 absolute error = 2.217454504460648e-07 relative error = 1.671695145980087e-06 % Correct digits = 8 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 = 4.296 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.68 Order of pole (six term test) = 2.838 TOP MAIN SOLVE Loop x[1] = 2.310000000002031 y[1] (analytic) = -13.24543315144892 y[1] (numeric) = -13.24543338053802 absolute error = 2.290890979139704e-07 relative error = 1.729570451147611e-06 % Correct digits = 8 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 = 4.306 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.75 Order of pole (six term test) = 2.841 TOP MAIN SOLVE Loop x[1] = 2.320000000002096 y[1] (analytic) = -13.22614537257476 y[1] (numeric) = -13.22614560900458 absolute error = 2.364298197221615e-07 relative error = 1.787594291927364e-06 % Correct digits = 8 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 = 4.316 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.82 Order of pole (six term test) = 2.845 TOP MAIN SOLVE Loop x[1] = 2.330000000002162 y[1] (analytic) = -13.20684291540386 y[1] (numeric) = -13.20684315917153 absolute error = 2.43767672714057e-07 relative error = 1.845767942236501e-06 % Correct digits = 8 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 = 4.326 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.89 Order of pole (six term test) = 2.848 TOP MAIN SOLVE Loop x[1] = 2.340000000002227 y[1] (analytic) = -13.18752578574454 y[1] (numeric) = -13.18752603684712 absolute error = 2.511025840590264e-07 relative error = 1.904091701041173e-06 % Correct digits = 8 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 = 4.336 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 29.96 Order of pole (six term test) = 2.852 TOP MAIN SOLVE Loop x[1] = 2.350000000002293 y[1] (analytic) = -13.16819398937653 y[1] (numeric) = -13.16819424781115 absolute error = 2.584346283640571e-07 relative error = 1.962566989615659e-06 % Correct digits = 8 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 = 4.346 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 30.03 Order of pole (six term test) = 2.855 TOP MAIN SOLVE Loop x[1] = 2.360000000002358 y[1] (analytic) = -13.14884753205121 y[1] (numeric) = -13.14884779781504 absolute error = 2.657638216163605e-07 relative error = 2.021194792688432e-06 % Correct digits = 8 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 = 4.356 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 30.11 Order of pole (six term test) = 2.859 TOP MAIN SOLVE Loop x[1] = 2.370000000002424 y[1] (analytic) = -13.12948641949177 y[1] (numeric) = -13.12948669258194 absolute error = 2.730901762504345e-07 relative error = 2.079976074654455e-06 % Correct digits = 8 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 = 4.366 Order of pole (three term test) = 1.54 Radius of convergence (six term test) for eq 1 = 30.18 Order of pole (six term test) = 2.862 TOP MAIN SOLVE Loop x[1] = 2.380000000002489 y[1] (analytic) = -13.11011065739331 y[1] (numeric) = -13.11011093780696 absolute error = 2.804136496337151e-07 relative error = 2.138911386499845e-06 % Correct digits = 8 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 = 4.376 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.25 Order of pole (six term test) = 2.866 TOP MAIN SOLVE Loop x[1] = 2.390000000002555 y[1] (analytic) = -13.09072025142308 y[1] (numeric) = -13.09072053915736 absolute error = 2.877342808460526e-07 relative error = 2.198001907609119e-06 % Correct digits = 8 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 = 4.386 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.32 Order of pole (six term test) = 2.869 TOP MAIN SOLVE Loop x[1] = 2.40000000000262 y[1] (analytic) = -13.0713152072206 y[1] (numeric) = -13.07131550227273 absolute error = 2.950521338362933e-07 relative error = 2.257249015564297e-06 % Correct digits = 8 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 = 4.396 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.39 Order of pole (six term test) = 2.873 TOP MAIN SOLVE Loop x[1] = 2.410000000002686 y[1] (analytic) = -13.05189553039784 y[1] (numeric) = -13.05189583276499 absolute error = 3.023671535373751e-07 relative error = 2.316653185226335e-06 % Correct digits = 8 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 = 4.406 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.46 Order of pole (six term test) = 2.876 TOP MAIN SOLVE Loop x[1] = 2.420000000002752 y[1] (analytic) = -13.03246122653935 y[1] (numeric) = -13.03246153621878 absolute error = 3.096794269907832e-07 relative error = 2.376215985666245e-06 % Correct digits = 8 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 = 4.416 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.53 Order of pole (six term test) = 2.88 TOP MAIN SOLVE Loop x[1] = 2.430000000002817 y[1] (analytic) = -13.01301230120247 y[1] (numeric) = -13.01301261819138 absolute error = 3.169889115639535e-07 relative error = 2.435937999802414e-06 % Correct digits = 8 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 = 4.426 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.61 Order of pole (six term test) = 2.884 TOP MAIN SOLVE Loop x[1] = 2.440000000002883 y[1] (analytic) = -12.99354875991743 y[1] (numeric) = -12.99354908421306 absolute error = 3.242956303495248e-07 relative error = 2.495820320849634e-06 % Correct digits = 8 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 = 4.436 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.68 Order of pole (six term test) = 2.887 TOP MAIN SOLVE Loop x[1] = 2.450000000002948 y[1] (analytic) = -12.97407060818754 y[1] (numeric) = -12.97407093978714 absolute error = 3.315995993347087e-07 relative error = 2.555863994800879e-06 % Correct digits = 8 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 = 4.446 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.75 Order of pole (six term test) = 2.891 TOP MAIN SOLVE Loop x[1] = 2.460000000003014 y[1] (analytic) = -12.95457785148934 y[1] (numeric) = -12.95457819039019 absolute error = 3.389008504939284e-07 relative error = 2.616070198342789e-06 % Correct digits = 8 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 = 4.456 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.82 Order of pole (six term test) = 2.894 TOP MAIN SOLVE Loop x[1] = 2.470000000003079 y[1] (analytic) = -12.93507049527275 y[1] (numeric) = -12.93507084147217 absolute error = 3.461994158016068e-07 relative error = 2.67644011625703e-06 % Correct digits = 8 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 = 4.466 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.89 Order of pole (six term test) = 2.898 TOP MAIN SOLVE Loop x[1] = 2.480000000003145 y[1] (analytic) = -12.91554854496122 y[1] (numeric) = -12.91554889845649 absolute error = 3.53495263283321e-07 relative error = 2.736974446363961e-06 % Correct digits = 8 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 = 4.476 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 30.97 Order of pole (six term test) = 2.902 TOP MAIN SOLVE Loop x[1] = 2.49000000000321 y[1] (analytic) = -12.89601200595188 y[1] (numeric) = -12.8960123667403 absolute error = 3.607884231371372e-07 relative error = 2.797674373834507e-06 % Correct digits = 8 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 = 4.485 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.04 Order of pole (six term test) = 2.905 TOP MAIN SOLVE Loop x[1] = 2.500000000003276 y[1] (analytic) = -12.87646088361569 y[1] (numeric) = -12.87646125169455 absolute error = 3.680788527304912e-07 relative error = 2.858540526448873e-06 % Correct digits = 8 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 = 4.495 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.11 Order of pole (six term test) = 2.909 TOP MAIN SOLVE Loop x[1] = 2.510000000003341 y[1] (analytic) = -12.8568951832976 y[1] (numeric) = -12.85689555866425 absolute error = 3.753666586447935e-07 relative error = 2.919574697415537e-06 % Correct digits = 8 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 = 4.505 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.18 Order of pole (six term test) = 2.913 TOP MAIN SOLVE Loop x[1] = 2.520000000003407 y[1] (analytic) = -12.83731491031666 y[1] (numeric) = -12.83731529296847 absolute error = 3.826518106819776e-07 relative error = 2.98077762643698e-06 % Correct digits = 8 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 = 4.515 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.26 Order of pole (six term test) = 2.916 TOP MAIN SOLVE Loop x[1] = 2.530000000003472 y[1] (analytic) = -12.81772006996625 y[1] (numeric) = -12.81772045990053 absolute error = 3.89934283973048e-07 relative error = 3.042150100365508e-06 % Correct digits = 8 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 = 4.525 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.33 Order of pole (six term test) = 2.92 TOP MAIN SOLVE Loop x[1] = 2.540000000003538 y[1] (analytic) = -12.7981106675141 y[1] (numeric) = -12.79811106472826 absolute error = 3.972141602304191e-07 relative error = 3.103693744723445e-06 % Correct digits = 8 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 = 4.535 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.4 Order of pole (six term test) = 2.924 TOP MAIN SOLVE Loop x[1] = 2.550000000003603 y[1] (analytic) = -12.77848670820256 y[1] (numeric) = -12.77848711269398 absolute error = 4.044914199141658e-07 relative error = 3.16540940371696e-06 % Correct digits = 8 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 = 4.545 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.47 Order of pole (six term test) = 2.928 TOP MAIN SOLVE Loop x[1] = 2.560000000003669 y[1] (analytic) = -12.75884819724865 y[1] (numeric) = -12.75884860901475 absolute error = 4.117661003277817e-07 relative error = 3.227298373348277e-06 % Correct digits = 8 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 = 4.555 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.55 Order of pole (six term test) = 2.931 TOP MAIN SOLVE Loop x[1] = 2.570000000003734 y[1] (analytic) = -12.73919513984426 y[1] (numeric) = -12.73919555888243 absolute error = 4.190381730495574e-07 relative error = 3.28936144277228e-06 % Correct digits = 8 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 = 4.565 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.62 Order of pole (six term test) = 2.935 TOP MAIN SOLVE Loop x[1] = 2.5800000000038 y[1] (analytic) = -12.71952754115624 y[1] (numeric) = -12.7195279674639 absolute error = 4.263076629484885e-07 relative error = 3.351599826087063e-06 % Correct digits = 8 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 = 4.575 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.69 Order of pole (six term test) = 2.939 TOP MAIN SOLVE Loop x[1] = 2.590000000003865 y[1] (analytic) = -12.6998454063266 y[1] (numeric) = -12.69984583990119 absolute error = 4.335745913408573e-07 relative error = 3.414014718044256e-06 % Correct digits = 8 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 = 4.585 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.77 Order of pole (six term test) = 2.943 TOP MAIN SOLVE Loop x[1] = 2.600000000003931 y[1] (analytic) = -12.68014874047259 y[1] (numeric) = -12.68014918131155 absolute error = 4.408389617793773e-07 relative error = 3.476607181840892e-06 % Correct digits = 8 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 = 4.595 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.84 Order of pole (six term test) = 2.946 TOP MAIN SOLVE Loop x[1] = 2.610000000003996 y[1] (analytic) = -12.66043754868686 y[1] (numeric) = -12.66043799678767 absolute error = 4.481008115675422e-07 relative error = 3.539378555001199e-06 % Correct digits = 8 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 = 4.605 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.91 Order of pole (six term test) = 2.95 TOP MAIN SOLVE Loop x[1] = 2.620000000004062 y[1] (analytic) = -12.64071183603763 y[1] (numeric) = -12.64071229139774 absolute error = 4.553601122836426e-07 relative error = 3.602329664579873e-06 % Correct digits = 8 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 = 4.615 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 31.98 Order of pole (six term test) = 2.954 TOP MAIN SOLVE Loop x[1] = 2.630000000004127 y[1] (analytic) = -12.62097160756876 y[1] (numeric) = -12.62097207018566 absolute error = 4.626168994548152e-07 relative error = 3.665461850634266e-06 % Correct digits = 8 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 = 4.625 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 32.06 Order of pole (six term test) = 2.958 TOP MAIN SOLVE Loop x[1] = 2.640000000004193 y[1] (analytic) = -12.60121686829994 y[1] (numeric) = -12.60121733817112 absolute error = 4.698711801864874e-07 relative error = 3.728776237226038e-06 % Correct digits = 8 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 = 4.635 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 32.13 Order of pole (six term test) = 2.962 TOP MAIN SOLVE Loop x[1] = 2.650000000004258 y[1] (analytic) = -12.5814476232268 y[1] (numeric) = -12.58144810034974 absolute error = 4.771229420441614e-07 relative error = 3.79227380133378e-06 % Correct digits = 8 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 = 4.645 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 32.21 Order of pole (six term test) = 2.966 TOP MAIN SOLVE Loop x[1] = 2.660000000004324 y[1] (analytic) = -12.56166387732101 y[1] (numeric) = -12.56166436169328 absolute error = 4.843722702929654e-07 relative error = 3.855956305019889e-06 % Correct digits = 8 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 = 4.655 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 32.28 Order of pole (six term test) = 2.969 TOP MAIN SOLVE Loop x[1] = 2.670000000004389 y[1] (analytic) = -12.5418656355305 y[1] (numeric) = -12.54186612714963 absolute error = 4.916191347348331e-07 relative error = 3.919824602028106e-06 % Correct digits = 8 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 = 4.665 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 32.35 Order of pole (six term test) = 2.973 TOP MAIN SOLVE Loop x[1] = 2.680000000004455 y[1] (analytic) = -12.52205290277949 y[1] (numeric) = -12.52205340164301 absolute error = 4.988635158298393e-07 relative error = 3.983879637811686e-06 % Correct digits = 8 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 = 4.675 Order of pole (three term test) = 1.541 Radius of convergence (six term test) for eq 1 = 32.43 Order of pole (six term test) = 2.977 TOP MAIN SOLVE Loop x[1] = 2.69000000000452 y[1] (analytic) = -12.50222568396869 y[1] (numeric) = -12.50222619007412 absolute error = 5.061054331179093e-07 relative error = 4.04812267760353e-06 % Correct digits = 8 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 = 4.685 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 32.5 Order of pole (six term test) = 2.981 TOP MAIN SOLVE Loop x[1] = 2.700000000004586 y[1] (analytic) = -12.48238398397537 y[1] (numeric) = -12.48238449732032 absolute error = 5.133449469951756e-07 relative error = 4.112555323199458e-06 % Correct digits = 8 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 = 4.695 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 32.57 Order of pole (six term test) = 2.985 TOP MAIN SOLVE Loop x[1] = 2.710000000004651 y[1] (analytic) = -12.46252780765356 y[1] (numeric) = -12.46252832823559 absolute error = 5.205820308162856e-07 relative error = 4.17717848939589e-06 % Correct digits = 8 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 = 4.705 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 32.65 Order of pole (six term test) = 2.989 TOP MAIN SOLVE Loop x[1] = 2.720000000004717 y[1] (analytic) = -12.44265715983411 y[1] (numeric) = -12.44265768765081 absolute error = 5.278166970157372e-07 relative error = 4.241993412143281e-06 % Correct digits = 8 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 = 4.715 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 32.72 Order of pole (six term test) = 2.993 TOP MAIN SOLVE Loop x[1] = 2.730000000004782 y[1] (analytic) = -12.42277204532484 y[1] (numeric) = -12.42277258037381 absolute error = 5.350489633570987e-07 relative error = 4.307001379442181e-06 % Correct digits = 8 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 = 4.725 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 32.8 Order of pole (six term test) = 2.997 TOP MAIN SOLVE Loop x[1] = 2.740000000004848 y[1] (analytic) = -12.40287246891068 y[1] (numeric) = -12.40287301118953 absolute error = 5.422788511566523e-07 relative error = 4.372203717452877e-06 % Correct digits = 8 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 = 4.735 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 32.87 Order of pole (six term test) = 3.001 TOP MAIN SOLVE Loop x[1] = 2.750000000004913 y[1] (analytic) = -12.38295843535377 y[1] (numeric) = -12.38295898486014 absolute error = 5.49506371072539e-07 relative error = 4.437601676055696e-06 % Correct digits = 8 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 = 4.745 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 32.95 Order of pole (six term test) = 3.005 TOP MAIN SOLVE Loop x[1] = 2.760000000004979 y[1] (analytic) = -12.36302994939357 y[1] (numeric) = -12.36303050612508 absolute error = 5.567315035648335e-07 relative error = 4.503196270200268e-06 % Correct digits = 8 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 = 4.755 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.02 Order of pole (six term test) = 3.009 TOP MAIN SOLVE Loop x[1] = 2.770000000005044 y[1] (analytic) = -12.34308701574705 y[1] (numeric) = -12.34308757970137 absolute error = 5.639543285695936e-07 relative error = 4.568989328602422e-06 % Correct digits = 8 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 = 4.765 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.09 Order of pole (six term test) = 3.013 TOP MAIN SOLVE Loop x[1] = 2.78000000000511 y[1] (analytic) = -12.3231296391087 y[1] (numeric) = -12.3231302102835 absolute error = 5.711747963488278e-07 relative error = 4.634981640833726e-06 % Correct digits = 8 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 = 4.775 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.17 Order of pole (six term test) = 3.017 TOP MAIN SOLVE Loop x[1] = 2.790000000005175 y[1] (analytic) = -12.30315782415078 y[1] (numeric) = -12.3031584025437 absolute error = 5.783929228897478e-07 relative error = 4.701174537112557e-06 % Correct digits = 8 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 = 4.785 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.24 Order of pole (six term test) = 3.021 TOP MAIN SOLVE Loop x[1] = 2.800000000005241 y[1] (analytic) = -12.28317157552332 y[1] (numeric) = -12.28317216113205 absolute error = 5.856087330613491e-07 relative error = 4.767569429936906e-06 % Correct digits = 8 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 = 4.795 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.32 Order of pole (six term test) = 3.025 TOP MAIN SOLVE Loop x[1] = 2.810000000005306 y[1] (analytic) = -12.26317089785431 y[1] (numeric) = -12.26317149067654 absolute error = 5.928222321927024e-07 relative error = 4.834167583006028e-06 % Correct digits = 8 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 = 4.805 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.39 Order of pole (six term test) = 3.029 TOP MAIN SOLVE Loop x[1] = 2.820000000005372 y[1] (analytic) = -12.2431557957498 y[1] (numeric) = -12.24315639578326 absolute error = 6.000334558109444e-07 relative error = 4.900970516272e-06 % Correct digits = 8 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 = 4.815 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.47 Order of pole (six term test) = 3.033 TOP MAIN SOLVE Loop x[1] = 2.830000000005437 y[1] (analytic) = -12.223126273794 y[1] (numeric) = -12.22312688103639 absolute error = 6.07242382599793e-07 relative error = 4.967979295949036e-06 % Correct digits = 8 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 = 4.825 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.54 Order of pole (six term test) = 3.037 TOP MAIN SOLVE Loop x[1] = 2.840000000005503 y[1] (analytic) = -12.20308233654943 y[1] (numeric) = -12.20308295099847 absolute error = 6.144490356518872e-07 relative error = 5.035195360532412e-06 % Correct digits = 8 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 = 4.835 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.62 Order of pole (six term test) = 3.041 TOP MAIN SOLVE Loop x[1] = 2.850000000005569 y[1] (analytic) = -12.18302398855699 y[1] (numeric) = -12.18302461021037 absolute error = 6.216533865455176e-07 relative error = 5.102619736523634e-06 % Correct digits = 8 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 = 4.845 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.69 Order of pole (six term test) = 3.045 TOP MAIN SOLVE Loop x[1] = 2.860000000005634 y[1] (analytic) = -12.1629512343361 y[1] (numeric) = -12.16295186319159 absolute error = 6.288554903477461e-07 relative error = 5.170254145001277e-06 % Correct digits = 8 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 = 4.855 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.77 Order of pole (six term test) = 3.049 TOP MAIN SOLVE Loop x[1] = 2.8700000000057 y[1] (analytic) = -12.14286407838482 y[1] (numeric) = -12.14286471444018 absolute error = 6.360553630457844e-07 relative error = 5.238099997989842e-06 % Correct digits = 8 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 = 4.865 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.85 Order of pole (six term test) = 3.053 TOP MAIN SOLVE Loop x[1] = 2.880000000005765 y[1] (analytic) = -12.12276252517994 y[1] (numeric) = -12.12276316843296 absolute error = 6.432530135214165e-07 relative error = 5.306158659672898e-06 % Correct digits = 8 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 = 4.875 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 33.92 Order of pole (six term test) = 3.057 TOP MAIN SOLVE Loop x[1] = 2.890000000005831 y[1] (analytic) = -12.10264657917713 y[1] (numeric) = -12.10264722962557 absolute error = 6.50448436445572e-07 relative error = 5.374431387302369e-06 % Correct digits = 8 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 = 4.885 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34 Order of pole (six term test) = 3.062 TOP MAIN SOLVE Loop x[1] = 2.900000000005896 y[1] (analytic) = -12.08251624481099 y[1] (numeric) = -12.08251690245266 absolute error = 6.576416744508151e-07 relative error = 5.442919844889503e-06 % Correct digits = 8 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 = 4.895 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.07 Order of pole (six term test) = 3.066 TOP MAIN SOLVE Loop x[1] = 2.910000000005962 y[1] (analytic) = -12.06237152649519 y[1] (numeric) = -12.06237219132789 absolute error = 6.648326937863658e-07 relative error = 5.511625075765988e-06 % Correct digits = 8 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 = 4.905 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.15 Order of pole (six term test) = 3.07 TOP MAIN SOLVE Loop x[1] = 2.920000000006027 y[1] (analytic) = -12.04221242862263 y[1] (numeric) = -12.04221310064414 absolute error = 6.720215104394356e-07 relative error = 5.580548544735318e-06 % Correct digits = 8 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 = 4.915 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.23 Order of pole (six term test) = 3.074 TOP MAIN SOLVE Loop x[1] = 2.930000000006093 y[1] (analytic) = -12.02203895556543 y[1] (numeric) = -12.02203963477358 absolute error = 6.792081492790203e-07 relative error = 5.649691801777024e-06 % Correct digits = 8 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 = 4.925 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.3 Order of pole (six term test) = 3.078 TOP MAIN SOLVE Loop x[1] = 2.940000000006158 y[1] (analytic) = -12.00185111167517 y[1] (numeric) = -12.0018517980678 absolute error = 6.863926227396178e-07 relative error = 5.719056305172025e-06 % Correct digits = 8 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 = 4.935 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.38 Order of pole (six term test) = 3.083 TOP MAIN SOLVE Loop x[1] = 2.950000000006224 y[1] (analytic) = -11.98164890128291 y[1] (numeric) = -11.98164959485784 absolute error = 6.93574930821228e-07 relative error = 5.788643420747915e-06 % Correct digits = 8 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 = 4.945 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.45 Order of pole (six term test) = 3.087 TOP MAIN SOLVE Loop x[1] = 2.960000000006289 y[1] (analytic) = -11.9614323286993 y[1] (numeric) = -11.96143302945437 absolute error = 7.0075506286571e-07 relative error = 5.858454435965619e-06 % Correct digits = 8 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 = 4.955 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.53 Order of pole (six term test) = 3.091 TOP MAIN SOLVE Loop x[1] = 2.970000000006355 y[1] (analytic) = -11.94120139821474 y[1] (numeric) = -11.9412021061478 absolute error = 7.079330615056278e-07 relative error = 5.928491094802798e-06 % Correct digits = 8 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 = 4.965 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.61 Order of pole (six term test) = 3.095 TOP MAIN SOLVE Loop x[1] = 2.98000000000642 y[1] (analytic) = -11.92095611409941 y[1] (numeric) = -11.92095682920835 absolute error = 7.151089409518363e-07 relative error = 5.998754916193739e-06 % Correct digits = 8 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 = 4.975 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.68 Order of pole (six term test) = 3.1 TOP MAIN SOLVE Loop x[1] = 2.990000000006486 y[1] (analytic) = -11.90069648060345 y[1] (numeric) = -11.90069720288615 absolute error = 7.222827012043354e-07 relative error = 6.069247311546515e-06 % Correct digits = 8 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 = 4.985 Order of pole (three term test) = 1.542 Radius of convergence (six term test) for eq 1 = 34.76 Order of pole (six term test) = 3.104 Finished! diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 100000 Total Elapsed Time = 2.0 Seconds Elapsed Time(since restart) = 2.0 Seconds Time to Timeout = 29 Minutes 58.0 Seconds Percent Done = 100 %