##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! // 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_max_h=0.0001; // 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(sin(sqrt(2.0*x+3.0))-sqrt(2.0*x+3.0)*cos(sqrt(2.0*x+3.0))); } // 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 = 9.919058284132172e-175 estimated_step_error = 9.919058284132172e-175 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 = 6.656566452983411e-167 estimated_step_error = 6.656566452983411e-167 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 = 4.467144945550478e-159 estimated_step_error = 4.467144945550478e-159 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 = 2.997848639133688e-151 estimated_step_error = 2.997848639133688e-151 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 = 2.011820036051395e-143 estimated_step_error = 2.011820036051395e-143 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.350106712941414e-135 estimated_step_error = 1.350106712941414e-135 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.060374406130706e-128 estimated_step_error = 9.060374406130706e-128 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.080262836331759e-120 estimated_step_error = 6.080262836331759e-120 best_h = 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 2.80289196959102 y[1] (numeric) = 2.80289196959102 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.995 Order of pole (six term test) = -1.363 TOP MAIN SOLVE Loop x[1] = 2.010000000000021 y[1] (analytic) = 2.807633062296792 y[1] (numeric) = 2.807633228570992 absolute error = 1.662741997421335e-07 relative error = 5.922219750686098e-06 % Correct digits = 8 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.002 Order of pole (six term test) = -1.364 TOP MAIN SOLVE Loop x[1] = 2.020000000000042 y[1] (analytic) = 2.812340890281396 y[1] (numeric) = 2.812341222929372 absolute error = 3.326479758314349e-07 relative error = 1.182815273144754e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.009 Order of pole (six term test) = -1.364 TOP MAIN SOLVE Loop x[1] = 2.030000000000063 y[1] (analytic) = 2.817015433909049 y[1] (numeric) = 2.817015933027591 absolute error = 4.991185420522015e-07 relative error = 1.771799103562584e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.016 Order of pole (six term test) = -1.364 TOP MAIN SOLVE Loop x[1] = 2.040000000000084 y[1] (analytic) = 2.821656674099247 y[1] (numeric) = 2.821657339782377 absolute error = 6.656831299522992e-07 relative error = 2.359192512904867e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.024 Order of pole (six term test) = -1.364 TOP MAIN SOLVE Loop x[1] = 2.050000000000106 y[1] (analytic) = 2.826264592323118 y[1] (numeric) = 2.826265424662112 absolute error = 8.323389937281434e-07 relative error = 2.945014405194037e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.031 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.060000000000127 y[1] (analytic) = 2.83083917059979 y[1] (numeric) = 2.83084016968319 absolute error = 9.990834000106474e-07 relative error = 3.529283508532788e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.038 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.070000000000148 y[1] (analytic) = 2.835380391492795 y[1] (numeric) = 2.835381557406431 absolute error = 1.165913636302918e-06 relative error = 4.112018407833729e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.045 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.080000000000169 y[1] (analytic) = 2.839888238106496 y[1] (numeric) = 2.839889570933503 absolute error = 1.33282700698345e-06 relative error = 4.69323753343236e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.052 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.09000000000019 y[1] (analytic) = 2.84436269408255 y[1] (numeric) = 2.844364193903386 absolute error = 1.499820835526577e-06 relative error = 5.272959171651437e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.06 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.100000000000211 y[1] (analytic) = 2.848803743596383 y[1] (numeric) = 2.848805410488842 absolute error = 1.666892459173397e-06 relative error = 5.851201448749435e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.067 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.110000000000232 y[1] (analytic) = 2.853211371353707 y[1] (numeric) = 2.853213205392947 absolute error = 1.834039240034002e-06 relative error = 6.427982372591772e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.074 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.120000000000253 y[1] (analytic) = 2.857585562587055 y[1] (numeric) = 2.857587563845603 absolute error = 2.001258547768003e-06 relative error = 7.003319774460948e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.081 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.130000000000274 y[1] (analytic) = 2.861926303052344 y[1] (numeric) = 2.861928471600121 absolute error = 2.168547777348095e-06 relative error = 7.577231373970965e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.088 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.140000000000295 y[1] (analytic) = 2.866233579025466 y[1] (numeric) = 2.866235914929801 absolute error = 2.335904335293293e-06 relative error = 8.149734733369193e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.096 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.150000000000317 y[1] (analytic) = 2.870507377298899 y[1] (numeric) = 2.870509880624546 absolute error = 2.503325647218446e-06 relative error = 8.720847286496213e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.103 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.160000000000338 y[1] (analytic) = 2.874747685178352 y[1] (numeric) = 2.874750355987507 absolute error = 2.670809154725617e-06 relative error = 9.29058633039622e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.11 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.170000000000359 y[1] (analytic) = 2.878954490479429 y[1] (numeric) = 2.878957328831745 absolute error = 2.838352316292259e-06 relative error = 9.858969030870617e-05 % Correct digits = 7 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.117 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.18000000000038 y[1] (analytic) = 2.883127781524316 y[1] (numeric) = 2.883130787476928 absolute error = 3.005952611268015e-06 relative error = 0.0001042601243875067 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.124 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.190000000000401 y[1] (analytic) = 2.887267547138503 y[1] (numeric) = 2.88727072074603 absolute error = 3.173607527440225e-06 relative error = 0.000109917334491066 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.131 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.200000000000422 y[1] (analytic) = 2.891373776647514 y[1] (numeric) = 2.891377117962087 absolute error = 3.341314572580245e-06 relative error = 0.0001155614884373209 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.138 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.210000000000443 y[1] (analytic) = 2.895446459873679 y[1] (numeric) = 2.895449968944953 absolute error = 3.509071273555264e-06 relative error = 0.0001211927529030655 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.145 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.220000000000464 y[1] (analytic) = 2.899485587132917 y[1] (numeric) = 2.899489264008081 absolute error = 3.676875163893811e-06 relative error = 0.0001268112930173106 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.152 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.230000000000485 y[1] (analytic) = 2.903491149231546 y[1] (numeric) = 2.903494993955354 absolute error = 3.844723808210659e-06 relative error = 0.0001324172732273775 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.16 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.240000000000506 y[1] (analytic) = 2.907463137463121 y[1] (numeric) = 2.907467150077893 absolute error = 4.012614772452849e-06 relative error = 0.0001380108562942613 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.167 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.250000000000528 y[1] (analytic) = 2.911401543605288 y[1] (numeric) = 2.911405724150934 absolute error = 4.18054564610415e-06 relative error = 0.0001435922040807617 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.174 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.260000000000549 y[1] (analytic) = 2.915306359916666 y[1] (numeric) = 2.915310708430699 absolute error = 4.348514033747364e-06 relative error = 0.0001491614772819851 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.181 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.27000000000057 y[1] (analytic) = 2.919177579133748 y[1] (numeric) = 2.919182095651297 absolute error = 4.516517548847077e-06 relative error = 0.0001547188352339748 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.188 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.280000000000591 y[1] (analytic) = 2.923015194467829 y[1] (numeric) = 2.923019879021658 absolute error = 4.684553828404603e-06 relative error = 0.000160264436437782 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.195 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.290000000000612 y[1] (analytic) = 2.926819199601953 y[1] (numeric) = 2.926824052222475 absolute error = 4.852620521411666e-06 relative error = 0.0001657984381840744 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.202 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.300000000000633 y[1] (analytic) = 2.93058958868788 y[1] (numeric) = 2.930594609403171 absolute error = 5.020715290626754e-06 relative error = 0.0001713209966351751 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.209 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.310000000000654 y[1] (analytic) = 2.93432635634308 y[1] (numeric) = 2.934331545178897 absolute error = 5.188835817016013e-06 relative error = 0.0001768322669971389 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.216 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.320000000000675 y[1] (analytic) = 2.938029497647745 y[1] (numeric) = 2.938034854627535 absolute error = 5.356979790427374e-06 relative error = 0.0001823324032218294 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.223 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.330000000000696 y[1] (analytic) = 2.941699008141823 y[1] (numeric) = 2.941704533286746 absolute error = 5.525144923357317e-06 relative error = 0.000187821558496135 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.23 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.340000000000718 y[1] (analytic) = 2.945334883822073 y[1] (numeric) = 2.94534057715101 absolute error = 5.693328936740016e-06 relative error = 0.0001932998847775148 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.237 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.350000000000739 y[1] (analytic) = 2.948937121139143 y[1] (numeric) = 2.948942982668712 absolute error = 5.861529569717305e-06 relative error = 0.0001987675331460801 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.244 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.36000000000076 y[1] (analytic) = 2.952505716994662 y[1] (numeric) = 2.952511746739233 absolute error = 6.029744571200979e-06 relative error = 0.0002042246535372883 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.370000000000781 y[1] (analytic) = 2.956040668738365 y[1] (numeric) = 2.956046866710077 absolute error = 6.197971711863204e-06 relative error = 0.0002096713951675263 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.258 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.380000000000802 y[1] (analytic) = 2.959541974165224 y[1] (numeric) = 2.959548340373996 absolute error = 6.366208772146109e-06 relative error = 0.0002151079061462468 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.264 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.390000000000823 y[1] (analytic) = 2.963009631512609 y[1] (numeric) = 2.963016165966155 absolute error = 6.53445354625859e-06 relative error = 0.000220534333630322 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.271 Order of pole (six term test) = -1.367 TOP MAIN SOLVE Loop x[1] = 2.400000000000844 y[1] (analytic) = 2.966443639457465 y[1] (numeric) = 2.966450342161306 absolute error = 6.702703840844038e-06 relative error = 0.0002259508237975457 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.278 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.410000000000865 y[1] (analytic) = 2.969843997113508 y[1] (numeric) = 2.969850868070992 absolute error = 6.870957483862128e-06 relative error = 0.0002313575221641353 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.285 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.420000000000886 y[1] (analytic) = 2.973210704028445 y[1] (numeric) = 2.973217743240754 absolute error = 7.039212309045695e-06 relative error = 0.0002367545730784626 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.292 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.430000000000907 y[1] (analytic) = 2.976543760181207 y[1] (numeric) = 2.976550967647374 absolute error = 7.207466167002963e-06 relative error = 0.0002421421201133016 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.299 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.440000000000929 y[1] (analytic) = 2.979843165979207 y[1] (numeric) = 2.979850541696132 absolute error = 7.375716925217546e-06 relative error = 0.0002475203060827468 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.306 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.45000000000095 y[1] (analytic) = 2.983108922255612 y[1] (numeric) = 2.983116466218068 absolute error = 7.54396245605804e-06 relative error = 0.0002528892726569917 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.313 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.460000000000971 y[1] (analytic) = 2.986341030266637 y[1] (numeric) = 2.986348742467294 absolute error = 7.712200657650214e-06 relative error = 0.0002582491610799597 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.319 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.470000000000992 y[1] (analytic) = 2.989539491688858 y[1] (numeric) = 2.989547372118287 absolute error = 7.880429428563929e-06 relative error = 0.0002636001113372848 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.326 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.480000000001013 y[1] (analytic) = 2.992704308616539 y[1] (numeric) = 2.992712357263231 absolute error = 8.048646691793948e-06 relative error = 0.0002689422629766808 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.333 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.490000000001034 y[1] (analytic) = 2.995835483558984 y[1] (numeric) = 2.995843700409365 absolute error = 8.216850380105001e-06 relative error = 0.0002742757546333475 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.34 Order of pole (six term test) = -1.364 TOP MAIN SOLVE Loop x[1] = 2.500000000001055 y[1] (analytic) = 2.998933019437902 y[1] (numeric) = 2.998941404476334 absolute error = 8.385038431146796e-06 relative error = 0.0002796007238840708 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.346 Order of pole (six term test) = -1.364 TOP MAIN SOLVE Loop x[1] = 2.510000000001076 y[1] (analytic) = 3.001996919584788 y[1] (numeric) = 3.002005472793596 absolute error = 8.55320880743804e-06 relative error = 0.0002849173079305174 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.353 Order of pole (six term test) = -1.364 TOP MAIN SOLVE Loop x[1] = 2.520000000001097 y[1] (analytic) = 3.005027187738331 y[1] (numeric) = 3.005035909097807 absolute error = 8.721359475938328e-06 relative error = 0.0002902256429334428 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.36 Order of pole (six term test) = -1.363 TOP MAIN SOLVE Loop x[1] = 2.530000000001118 y[1] (analytic) = 3.008023828041829 y[1] (numeric) = 3.008032717530253 absolute error = 8.889488424479453e-06 relative error = 0.0002955258645762242 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.367 Order of pole (six term test) = -1.363 TOP MAIN SOLVE Loop x[1] = 2.54000000000114 y[1] (analytic) = 3.010986845040628 y[1] (numeric) = 3.010995902634276 absolute error = 9.05759364799863e-06 relative error = 0.0003008181076220017 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.373 Order of pole (six term test) = -1.363 TOP MAIN SOLVE Loop x[1] = 2.550000000001161 y[1] (analytic) = 3.013916243679576 y[1] (numeric) = 3.013925469352729 absolute error = 9.225673152535308e-06 relative error = 0.0003061025060627442 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.38 Order of pole (six term test) = -1.362 TOP MAIN SOLVE Loop x[1] = 2.560000000001182 y[1] (analytic) = 3.016812029300495 y[1] (numeric) = 3.016821423025455 absolute error = 9.393724960116145e-06 relative error = 0.0003113791932967816 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.387 Order of pole (six term test) = -1.362 TOP MAIN SOLVE Loop x[1] = 2.570000000001203 y[1] (analytic) = 3.019674207639666 y[1] (numeric) = 3.019683769386775 absolute error = 9.561747109643193e-06 relative error = 0.0003166483021728742 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.393 Order of pole (six term test) = -1.362 TOP MAIN SOLVE Loop x[1] = 2.580000000001224 y[1] (analytic) = 3.022502784825337 y[1] (numeric) = 3.022512514562981 absolute error = 9.729737643127123e-06 relative error = 0.0003219099645491106 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.4 Order of pole (six term test) = -1.361 TOP MAIN SOLVE Loop x[1] = 2.590000000001245 y[1] (analytic) = 3.025297767375247 y[1] (numeric) = 3.025307665069865 absolute error = 9.897694617233554e-06 relative error = 0.0003271643116909053 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.407 Order of pole (six term test) = -1.361 TOP MAIN SOLVE Loop x[1] = 2.600000000001266 y[1] (analytic) = 3.02805916219416 y[1] (numeric) = 3.028069227810266 absolute error = 1.006561610594758e-05 relative error = 0.000332411474373372 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.413 Order of pole (six term test) = -1.36 TOP MAIN SOLVE Loop x[1] = 2.610000000001287 y[1] (analytic) = 3.030786976571416 y[1] (numeric) = 3.030797210071608 absolute error = 1.0233500191692e-05 relative error = 0.0003376515826021091 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.42 Order of pole (six term test) = -1.36 TOP MAIN SOLVE Loop x[1] = 2.620000000001308 y[1] (analytic) = 3.033481218178512 y[1] (numeric) = 3.033491619523486 absolute error = 1.040134497376499e-05 relative error = 0.0003428847659063667 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.426 Order of pole (six term test) = -1.359 TOP MAIN SOLVE Loop x[1] = 2.630000000001329 y[1] (analytic) = 3.036141895066679 y[1] (numeric) = 3.036152464215232 absolute error = 1.0569148552797e-05 relative error = 0.0003481111528407301 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.433 Order of pole (six term test) = -1.359 TOP MAIN SOLVE Loop x[1] = 2.640000000001351 y[1] (analytic) = 3.03876901566449 y[1] (numeric) = 3.038779752573538 absolute error = 1.073690904851432e-05 relative error = 0.0003533308715853966 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.439 Order of pole (six term test) = -1.358 TOP MAIN SOLVE Loop x[1] = 2.650000000001372 y[1] (analytic) = 3.041362588775474 y[1] (numeric) = 3.041373493400068 absolute error = 1.090462459441e-05 relative error = 0.0003585440497839641 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.446 Order of pole (six term test) = -1.358 TOP MAIN SOLVE Loop x[1] = 2.660000000001393 y[1] (analytic) = 3.043922623575755 y[1] (numeric) = 3.043933695869091 absolute error = 1.107229333641158e-05 relative error = 0.0003637508145133051 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.453 Order of pole (six term test) = -1.357 TOP MAIN SOLVE Loop x[1] = 2.670000000001414 y[1] (analytic) = 3.046449129611695 y[1] (numeric) = 3.046460369525121 absolute error = 1.123991342577568e-05 relative error = 0.000368951292064028 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.459 Order of pole (six term test) = -1.357 TOP MAIN SOLVE Loop x[1] = 2.680000000001435 y[1] (analytic) = 3.048942116797563 y[1] (numeric) = 3.048953524280591 absolute error = 1.140748302841388e-05 relative error = 0.0003741456082608632 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.466 Order of pole (six term test) = -1.356 TOP MAIN SOLVE Loop x[1] = 2.690000000001456 y[1] (analytic) = 3.051401595413211 y[1] (numeric) = 3.051413170413535 absolute error = 1.157500032400449e-05 relative error = 0.0003793338884466645 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472 Order of pole (six term test) = -1.356 TOP MAIN SOLVE Loop x[1] = 2.700000000001477 y[1] (analytic) = 3.053827576101776 y[1] (numeric) = 3.053839318565277 absolute error = 1.174246350155173e-05 relative error = 0.0003845162573500967 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.479 Order of pole (six term test) = -1.355 TOP MAIN SOLVE Loop x[1] = 2.710000000001498 y[1] (analytic) = 3.056220069867378 y[1] (numeric) = 3.056231979738137 absolute error = 1.190987075938565e-05 relative error = 0.0003896928390991973 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.485 Order of pole (six term test) = -1.354 TOP MAIN SOLVE Loop x[1] = 2.720000000001519 y[1] (analytic) = 3.058579088072854 y[1] (numeric) = 3.058591165293167 absolute error = 1.207722031271175e-05 relative error = 0.0003948637574816267 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.492 Order of pole (six term test) = -1.354 TOP MAIN SOLVE Loop x[1] = 2.730000000001541 y[1] (analytic) = 3.060904642437493 y[1] (numeric) = 3.060916886947878 absolute error = 1.224451038428498e-05 relative error = 0.0004000291356523376 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.499 Order of pole (six term test) = -1.353 TOP MAIN SOLVE Loop x[1] = 2.740000000001562 y[1] (analytic) = 3.063196745034792 y[1] (numeric) = 3.063209156773999 absolute error = 1.241173920707439e-05 relative error = 0.0004051890962339547 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.505 Order of pole (six term test) = -1.353 TOP MAIN SOLVE Loop x[1] = 2.750000000001583 y[1] (analytic) = 3.065455408290216 y[1] (numeric) = 3.065467987195242 absolute error = 1.257890502603942e-05 relative error = 0.0004103437613876567 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.512 Order of pole (six term test) = -1.352 TOP MAIN SOLVE Loop x[1] = 2.760000000001604 y[1] (analytic) = 3.067680644978992 y[1] (numeric) = 3.067693390985093 absolute error = 1.274600610035037e-05 relative error = 0.0004154932528981568 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.518 Order of pole (six term test) = -1.351 TOP MAIN SOLVE Loop x[1] = 2.770000000001625 y[1] (analytic) = 3.069872468223898 y[1] (numeric) = 3.069885381264595 absolute error = 1.291304069717114e-05 relative error = 0.0004206376919834098 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.525 Order of pole (six term test) = -1.351 TOP MAIN SOLVE Loop x[1] = 2.780000000001646 y[1] (analytic) = 3.07203089149307 y[1] (numeric) = 3.072043971500165 absolute error = 1.308000709476786e-05 relative error = 0.0004257771994086528 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.532 Order of pole (six term test) = -1.35 TOP MAIN SOLVE Loop x[1] = 2.790000000001667 y[1] (analytic) = 3.074155928597837 y[1] (numeric) = 3.074169175501418 absolute error = 1.324690358162073e-05 relative error = 0.0004309118954698832 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.539 Order of pole (six term test) = -1.349 TOP MAIN SOLVE Loop x[1] = 2.800000000001688 y[1] (analytic) = 3.076247593690546 y[1] (numeric) = 3.076261007419004 absolute error = 1.341372845864441e-05 relative error = 0.0004360419000784033 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.546 Order of pole (six term test) = -1.348 TOP MAIN SOLVE Loop x[1] = 2.810000000001709 y[1] (analytic) = 3.078305901262423 y[1] (numeric) = 3.07831948174246 absolute error = 1.358048003652357e-05 relative error = 0.000441167332686273 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.553 Order of pole (six term test) = -1.348 TOP MAIN SOLVE Loop x[1] = 2.82000000000173 y[1] (analytic) = 3.080330866141435 y[1] (numeric) = 3.080344613298077 absolute error = 1.374715664148596e-05 relative error = 0.0004462883124859338 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.56 Order of pole (six term test) = -1.347 TOP MAIN SOLVE Loop x[1] = 2.830000000001752 y[1] (analytic) = 3.082322503490167 y[1] (numeric) = 3.082336417246764 absolute error = 1.391375659665073e-05 relative error = 0.0004514049578165796 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.567 Order of pole (six term test) = -1.346 TOP MAIN SOLVE Loop x[1] = 2.840000000001773 y[1] (analytic) = 3.084280828803716 y[1] (numeric) = 3.084294909081966 absolute error = 1.408027825045011e-05 relative error = 0.0004565173870990001 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.574 Order of pole (six term test) = -1.345 TOP MAIN SOLVE Loop x[1] = 2.850000000001794 y[1] (analytic) = 3.086205857907592 y[1] (numeric) = 3.08622010462755 absolute error = 1.424671995797766e-05 relative error = 0.0004616257182415159 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.581 Order of pole (six term test) = -1.345 TOP MAIN SOLVE Loop x[1] = 2.860000000001815 y[1] (analytic) = 3.088097606955643 y[1] (numeric) = 3.088112020035721 absolute error = 1.441308007743558e-05 relative error = 0.0004667300685370664 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.589 Order of pole (six term test) = -1.344 TOP MAIN SOLVE Loop x[1] = 2.870000000001836 y[1] (analytic) = 3.089956092427978 y[1] (numeric) = 3.089970671784963 absolute error = 1.457935698523372e-05 relative error = 0.0004718305551642248 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.597 Order of pole (six term test) = -1.343 TOP MAIN SOLVE Loop x[1] = 2.880000000001857 y[1] (analytic) = 3.091781331128915 y[1] (numeric) = 3.09179607667798 absolute error = 1.474554906533143e-05 relative error = 0.0004769272948532659 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.605 Order of pole (six term test) = -1.342 TOP MAIN SOLVE Loop x[1] = 2.890000000001878 y[1] (analytic) = 3.093573340184939 y[1] (numeric) = 3.093588251839652 absolute error = 1.491165471323441e-05 relative error = 0.0004820204040271102 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.613 Order of pole (six term test) = -1.341 TOP MAIN SOLVE Loop x[1] = 2.900000000001899 y[1] (analytic) = 3.095332137042667 y[1] (numeric) = 3.095347214714997 absolute error = 1.507767233066559e-05 relative error = 0.0004871099986404386 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.621 Order of pole (six term test) = -1.34 TOP MAIN SOLVE Loop x[1] = 2.91000000000192 y[1] (analytic) = 3.097057739466831 y[1] (numeric) = 3.097072983067165 absolute error = 1.524360033400285e-05 relative error = 0.0004921961944638167 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.63 Order of pole (six term test) = -1.339 TOP MAIN SOLVE Loop x[1] = 2.920000000001941 y[1] (analytic) = 3.098750165538275 y[1] (numeric) = 3.098765574975423 absolute error = 1.540943714717358e-05 relative error = 0.0004972791068652302 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.639 Order of pole (six term test) = -1.339 TOP MAIN SOLVE Loop x[1] = 2.930000000001963 y[1] (analytic) = 3.100409433651958 y[1] (numeric) = 3.100425008833164 absolute error = 1.557518120653967e-05 relative error = 0.0005023588509790377 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.648 Order of pole (six term test) = -1.338 TOP MAIN SOLVE Loop x[1] = 2.940000000001984 y[1] (analytic) = 3.102035562514973 y[1] (numeric) = 3.102051303345926 absolute error = 1.574083095290391e-05 relative error = 0.0005074355414591713 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.737 Order of pole (three term test) = 4.287 Radius of convergence (six term test) for eq 1 = 4.658 Order of pole (six term test) = -1.337 TOP MAIN SOLVE Loop x[1] = 2.950000000002005 y[1] (analytic) = 3.103628571144579 y[1] (numeric) = 3.103644477529419 absolute error = 1.590638483994766e-05 relative error = 0.0005125092927624902 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.399 Order of pole (three term test) = 3.087 Radius of convergence (six term test) for eq 1 = 4.668 Order of pole (six term test) = -1.336 TOP MAIN SOLVE Loop x[1] = 2.960000000002026 y[1] (analytic) = 3.105188478866244 y[1] (numeric) = 3.10520455070758 absolute error = 1.607184133600725e-05 relative error = 0.0005175802192166883 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.135 Order of pole (three term test) = 2.15 Radius of convergence (six term test) for eq 1 = 4.679 Order of pole (six term test) = -1.335 TOP MAIN SOLVE Loop x[1] = 2.970000000002047 y[1] (analytic) = 3.106715305311697 y[1] (numeric) = 3.106731542510605 absolute error = 1.623719890853081e-05 relative error = 0.0005226484345304932 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.924 Order of pole (three term test) = 1.404 Radius of convergence (six term test) for eq 1 = 4.691 Order of pole (six term test) = -1.334 TOP MAIN SOLVE Loop x[1] = 2.980000000002068 y[1] (analytic) = 3.108209070416997 y[1] (numeric) = 3.108225472873042 absolute error = 1.640245604539459e-05 relative error = 0.0005277140524911356 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.753 Order of pole (three term test) = 0.799 Radius of convergence (six term test) for eq 1 = 4.703 Order of pole (six term test) = -1.333 TOP MAIN SOLVE Loop x[1] = 2.990000000002089 y[1] (analytic) = 3.10966979442061 y[1] (numeric) = 3.10968636203185 absolute error = 1.656761123980388e-05 relative error = 0.0005327771864887261 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.612 Order of pole (three term test) = 0.3014 Radius of convergence (six term test) for eq 1 = 4.716 Order of pole (six term test) = -1.332 Finished! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 10000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 30 Minutes 0.0 Seconds Percent Done = 100 %