##############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=40; ! /* 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_min_h=0.001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; 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 = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000 step_error = 7.905694150420948e-14 est_needed_step_err = 7.905694150420948e-14 opt_iter = 1 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.998 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 min_size = 13.83604079041925 glob_desired_digits_correct = 10 estimated_h = 0.001 estimated_answer = 13.83604079041925 desired_abs_gbl_error = 1.383604079041926e-09 range = 1 estimated_steps = 1000 step_error = 1.093835067418032e-12 est_needed_step_err = 1.093835067418032e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.842989914279855e-134 estimated_step_error = 2.842989914279855e-134 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.998 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 min_size = 13.83604079041925 glob_desired_digits_correct = 10 estimated_h = 0.002 estimated_answer = 13.83604079041925 desired_abs_gbl_error = 1.383604079041926e-09 range = 1 estimated_steps = 500 step_error = 1.546916387341869e-12 est_needed_step_err = 1.546916387341869e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.953460210014427e-123 estimated_step_error = 1.953460210014427e-123 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.998 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 min_size = 13.83604079041925 glob_desired_digits_correct = 10 estimated_h = 0.004 estimated_answer = 13.83604079041925 desired_abs_gbl_error = 1.383604079041926e-09 range = 1 estimated_steps = 250 step_error = 2.187670134836063e-12 est_needed_step_err = 2.187670134836063e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.342094956730691e-112 estimated_step_error = 1.342094956730691e-112 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.998 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 min_size = 13.83604079041925 glob_desired_digits_correct = 10 estimated_h = 0.008 estimated_answer = 13.83604079041925 desired_abs_gbl_error = 1.383604079041926e-09 range = 1 estimated_steps = 125 step_error = 3.093832774683737e-12 est_needed_step_err = 3.093832774683737e-12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.218511911449003e-102 estimated_step_error = 9.218511911449003e-102 Double H and LOOP opt_iter = 5 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.499 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 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 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.998 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = -13.8172110836278 y[1] (numeric) = -13.81721852574161 absolute error = 7.442113815869789e-06 relative error = 5.386118639157255e-05 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 7 h = 0.01 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.008 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = -13.79836650334326 y[1] (numeric) = -13.79838138415804 absolute error = 1.488081477596381e-05 relative error = 0.0001078447566410001 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.018 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.029999999999999 y[1] (analytic) = -13.77950705634998 y[1] (numeric) = -13.77952937247024 absolute error = 2.231612025305196e-05 relative error = 0.0001619515136629511 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.028 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.039999999999999 y[1] (analytic) = -13.76063274939781 y[1] (numeric) = -13.76066249744533 absolute error = 2.974804751154636e-05 relative error = 0.0002161822646770962 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.038 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.049999999999999 y[1] (analytic) = -13.74174358920231 y[1] (numeric) = -13.74178076581602 absolute error = 3.717661370750136e-05 relative error = 0.0002705378212464478 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.048 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.059999999999999 y[1] (analytic) = -13.72283958244499 y[1] (numeric) = -13.72288418428088 absolute error = 4.460183588328448e-05 relative error = 0.0003250189992772457 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.058 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.069999999999999 y[1] (analytic) = -13.7039207357735 y[1] (numeric) = -13.70397275950449 absolute error = 5.202373098533997e-05 relative error = 0.0003796266191874143 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.068 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.079999999999998 y[1] (analytic) = -13.68498705580186 y[1] (numeric) = -13.6850464981177 absolute error = 5.944231584109616e-05 relative error = 0.0004343615057779328 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.078 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.089999999999998 y[1] (analytic) = -13.66603854911067 y[1] (numeric) = -13.66610540671785 absolute error = 6.68576071749527e-05 relative error = 0.0004892244883891646 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.088 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.099999999999998 y[1] (analytic) = -13.6470752222473 y[1] (numeric) = -13.64714949186892 absolute error = 7.426962162426776e-05 relative error = 0.0005442164010585528 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.098 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.109999999999998 y[1] (analytic) = -13.62809708172612 y[1] (numeric) = -13.62817876010181 absolute error = 8.167837569672542e-05 relative error = 0.000599338082249559 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.108 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.119999999999997 y[1] (analytic) = -13.60910413402868 y[1] (numeric) = -13.6091932179145 absolute error = 8.908388581474469e-05 relative error = 0.0006545903752179852 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.118 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.129999999999997 y[1] (analytic) = -13.59009638560396 y[1] (numeric) = -13.59019287177225 absolute error = 9.648616829238676e-05 relative error = 0.0007099741278847364 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.128 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.139999999999997 y[1] (analytic) = -13.57107384286849 y[1] (numeric) = -13.57117772810784 absolute error = 0.0001038852393513423 relative error = 0.000765490192995548 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.138 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.149999999999997 y[1] (analytic) = -13.55203651220663 y[1] (numeric) = -13.55214779332173 absolute error = 0.0001112811151013915 relative error = 0.0008211394280199735 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.148 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.159999999999997 y[1] (analytic) = -13.53298439997074 y[1] (numeric) = -13.5331030737823 absolute error = 0.0001186738115563912 relative error = 0.000876922695312113 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.158 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.169999999999996 y[1] (analytic) = -13.51391751248136 y[1] (numeric) = -13.514043575826 absolute error = 0.0001260633446396042 relative error = 0.0009328408621939047 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.168 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.179999999999996 y[1] (analytic) = -13.49483585602742 y[1] (numeric) = -13.49496930575759 absolute error = 0.0001334497301730408 relative error = 0.0009888948009207242 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.178 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.189999999999996 y[1] (analytic) = -13.47573943686642 y[1] (numeric) = -13.4758802698503 absolute error = 0.0001408329838756828 relative error = 0.001045085388712676 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.188 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199999999999996 y[1] (analytic) = -13.45662826122466 y[1] (numeric) = -13.45677647434603 absolute error = 0.0001482131213759175 relative error = 0.001101413507891827 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.198 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.209999999999996 y[1] (analytic) = -13.43750233529737 y[1] (numeric) = -13.43765792545558 absolute error = 0.0001555901582079855 relative error = 0.001157880045901717 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.208 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.219999999999995 y[1] (analytic) = -13.41836166524894 y[1] (numeric) = -13.41852462935875 absolute error = 0.0001629641098137569 relative error = 0.001214485895366821 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.218 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.229999999999995 y[1] (analytic) = -13.3992062572131 y[1] (numeric) = -13.39937659220464 absolute error = 0.0001703349915356256 relative error = 0.001271231954086313 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.228 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.239999999999995 y[1] (analytic) = -13.3800361172931 y[1] (numeric) = -13.38021382011173 absolute error = 0.0001777028186324969 relative error = 0.001328119125200446 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.238 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.249999999999995 y[1] (analytic) = -13.3608512515619 y[1] (numeric) = -13.36103631916816 absolute error = 0.0001850676062584711 relative error = 0.001385148317079247 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.248 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.259999999999994 y[1] (analytic) = -13.34165166606232 y[1] (numeric) = -13.34184409543181 absolute error = 0.0001924293694859358 relative error = 0.001442320443543177 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.258 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.269999999999994 y[1] (analytic) = -13.32243736680728 y[1] (numeric) = -13.32263715493058 absolute error = 0.0001997881233002374 relative error = 0.001499636423872463 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.268 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.279999999999994 y[1] (analytic) = -13.30320835977992 y[1] (numeric) = -13.30341550366251 absolute error = 0.0002071438825854699 relative error = 0.001557097182749806 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.278 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.289999999999994 y[1] (analytic) = -13.28396465093382 y[1] (numeric) = -13.28417914759597 absolute error = 0.0002144966621493438 relative error = 0.001614703650496882 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.288 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.299999999999994 y[1] (analytic) = -13.26470624619315 y[1] (numeric) = -13.26492809266985 absolute error = 0.0002218464767018702 relative error = 0.00167245676296479 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.298 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.309999999999993 y[1] (analytic) = -13.24543315145285 y[1] (numeric) = -13.24566234479372 absolute error = 0.0002291933408695712 relative error = 0.001730357461691856 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.308 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.319999999999993 y[1] (analytic) = -13.22614537257881 y[1] (numeric) = -13.22638190984801 absolute error = 0.000236537269193704 relative error = 0.001788406693942033 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.318 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.329999999999993 y[1] (analytic) = -13.20684291540805 y[1] (numeric) = -13.20708679368417 absolute error = 0.0002438782761249314 relative error = 0.001846605412716809 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.328 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.339999999999993 y[1] (analytic) = -13.18752578574885 y[1] (numeric) = -13.18777700212489 absolute error = 0.0002512163760393094 relative error = 0.001904954576928959 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.338 Order of pole (three term test) = 1.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.349999999999993 y[1] (analytic) = -13.16819398938097 y[1] (numeric) = -13.16845254096419 absolute error = 0.0002585515832116414 relative error = 0.00196345515125416 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.348 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.359999999999992 y[1] (analytic) = -13.14884753205579 y[1] (numeric) = -13.14911341596764 absolute error = 0.0002658839118527823 relative error = 0.002022108106467731 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.358 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.369999999999992 y[1] (analytic) = -13.12948641949648 y[1] (numeric) = -13.12975963287255 absolute error = 0.0002732133760687816 relative error = 0.002080914419189136 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.368 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.379999999999992 y[1] (analytic) = -13.11011065739815 y[1] (numeric) = -13.11039119738805 absolute error = 0.0002805399899017402 relative error = 0.00213987507224761 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.378 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.389999999999992 y[1] (analytic) = -13.09072025142805 y[1] (numeric) = -13.09100811519535 absolute error = 0.0002878637673049411 relative error = 0.00219899105454903 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.388 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999991 y[1] (analytic) = -13.0713152072257 y[1] (numeric) = -13.07161039194785 absolute error = 0.0002951847221464021 relative error = 0.002258263361159149 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.398 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.409999999999991 y[1] (analytic) = -13.05189553040307 y[1] (numeric) = -13.05219803327129 absolute error = 0.0003025028682159814 relative error = 0.002317692993414876 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.408 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.419999999999991 y[1] (analytic) = -13.03246122654472 y[1] (numeric) = -13.03277104476395 absolute error = 0.0003098182192360355 relative error = 0.002377280959063918 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.418 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.429999999999991 y[1] (analytic) = -13.01301230120797 y[1] (numeric) = -13.01332943199679 absolute error = 0.0003171307888241159 relative error = 0.002437028272037193 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.428 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.439999999999991 y[1] (analytic) = -12.99354875992306 y[1] (numeric) = -12.9938732005136 absolute error = 0.00032444059054626 relative error = 0.002496935952916539 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.438 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44999999999999 y[1] (analytic) = -12.9740706081933 y[1] (numeric) = -12.97440235583118 absolute error = 0.0003317476378743578 relative error = 0.002557005028667369 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.448 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45999999999999 y[1] (analytic) = -12.95457785149524 y[1] (numeric) = -12.95491690343944 absolute error = 0.0003390519442056927 relative error = 0.002617236532848956 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.458 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46999999999999 y[1] (analytic) = -12.93507049527878 y[1] (numeric) = -12.93541684880164 absolute error = 0.0003463535228611647 relative error = 0.002677631505661925 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.468 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47999999999999 y[1] (analytic) = -12.91554854496739 y[1] (numeric) = -12.91590219735447 absolute error = 0.0003536523870888431 relative error = 0.002738190994037536 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.478 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48999999999999 y[1] (analytic) = -12.89601200595818 y[1] (numeric) = -12.89637295450824 absolute error = 0.0003609485500586374 relative error = 0.002798916051659017 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.488 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499999999999989 y[1] (analytic) = -12.87646088362212 y[1] (numeric) = -12.87682912564699 absolute error = 0.0003682420248676266 relative error = 0.002859807739065961 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.498 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.509999999999989 y[1] (analytic) = -12.85689518330415 y[1] (numeric) = -12.85727071612869 absolute error = 0.0003755328245382827 relative error = 0.002920867123704533 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.508 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.519999999999989 y[1] (analytic) = -12.83731491032336 y[1] (numeric) = -12.83769773128537 absolute error = 0.0003828209620131418 relative error = 0.002982095279950556 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.518 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.529999999999989 y[1] (analytic) = -12.81772006997307 y[1] (numeric) = -12.81811017642324 absolute error = 0.0003901064501654616 relative error = 0.003043493289257651 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.528 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.539999999999988 y[1] (analytic) = -12.79811066752107 y[1] (numeric) = -12.79850805682287 absolute error = 0.0003973893018009989 relative error = 0.003105062240237459 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.538 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.549999999999988 y[1] (analytic) = -12.77848670820966 y[1] (numeric) = -12.77889137773931 absolute error = 0.0004046695296491265 relative error = 0.003166803228657293 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.548 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.559999999999988 y[1] (analytic) = -12.75884819725589 y[1] (numeric) = -12.75926014440225 absolute error = 0.0004119471463663871 relative error = 0.003228717357535351 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.558 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.569999999999988 y[1] (analytic) = -12.73919513985162 y[1] (numeric) = -12.73961436201617 absolute error = 0.0004192221645453742 relative error = 0.00329080573727876 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.568 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.579999999999988 y[1] (analytic) = -12.71952754116374 y[1] (numeric) = -12.71995403576044 absolute error = 0.0004264945966969691 relative error = 0.00335306948561352 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.578 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.589999999999987 y[1] (analytic) = -12.69984540633423 y[1] (numeric) = -12.70027917078951 absolute error = 0.0004337644552716569 relative error = 0.003415509727821651 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.588 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.599999999999987 y[1] (analytic) = -12.68014874048035 y[1] (numeric) = -12.680589772233 absolute error = 0.0004410317526506446 relative error = 0.003478127596742508 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.598 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.609999999999987 y[1] (analytic) = -12.66043754869476 y[1] (numeric) = -12.6608858451959 absolute error = 0.0004482965011387563 relative error = 0.003540924232788256 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.608 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.619999999999987 y[1] (analytic) = -12.64071183604567 y[1] (numeric) = -12.64116739475864 absolute error = 0.0004555587129750904 relative error = 0.003603900784100151 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.618 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.629999999999987 y[1] (analytic) = -12.62097160757694 y[1] (numeric) = -12.62143442597727 absolute error = 0.0004628184003365732 relative error = 0.003667058406650107 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.628 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.639999999999986 y[1] (analytic) = -12.60121686830826 y[1] (numeric) = -12.60168694388358 absolute error = 0.0004700755753273 relative error = 0.003730398264230563 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.638 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.649999999999986 y[1] (analytic) = -12.58144762323524 y[1] (numeric) = -12.58192495348523 absolute error = 0.0004773302499927468 relative error = 0.003793921528642061 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.648 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.659999999999986 y[1] (analytic) = -12.5616638773296 y[1] (numeric) = -12.5621484597659 absolute error = 0.0004845824363020057 relative error = 0.00385762937962817 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.658 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.669999999999986 y[1] (analytic) = -12.54186563553922 y[1] (numeric) = -12.54235746768538 absolute error = 0.0004918321461619968 relative error = 0.003921523005064877 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.668 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.679999999999986 y[1] (analytic) = -12.52205290278835 y[1] (numeric) = -12.52255198217977 absolute error = 0.0004990793914174674 relative error = 0.003985603601038412 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.678 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.689999999999985 y[1] (analytic) = -12.50222568397768 y[1] (numeric) = -12.50273200816153 absolute error = 0.0005063241838509924 relative error = 0.004049872371923953 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.688 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.699999999999985 y[1] (analytic) = -12.4823839839845 y[1] (numeric) = -12.48289755051967 absolute error = 0.0005135665351669871 relative error = 0.004114330530337134 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.698 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.709999999999985 y[1] (analytic) = -12.46252780766283 y[1] (numeric) = -12.46304861411986 absolute error = 0.0005208064570272342 relative error = 0.004178979297498587 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.708 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.719999999999985 y[1] (analytic) = -12.44265715984352 y[1] (numeric) = -12.44318520380453 absolute error = 0.000528043961008251 relative error = 0.004243819902973938 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.718 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.729999999999984 y[1] (analytic) = -12.42277204533439 y[1] (numeric) = -12.42330732439304 absolute error = 0.000535279058645699 relative error = 0.004308853585112135 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.728 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.739999999999984 y[1] (analytic) = -12.40287246892037 y[1] (numeric) = -12.40341498068176 absolute error = 0.0005425117613935271 relative error = 0.004374081590800644 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.738 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.749999999999984 y[1] (analytic) = -12.38295843536359 y[1] (numeric) = -12.38350817744425 absolute error = 0.0005497420806577225 relative error = 0.004439505175820943 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.748 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.759999999999984 y[1] (analytic) = -12.36302994940353 y[1] (numeric) = -12.36358691943131 absolute error = 0.0005569700277732181 relative error = 0.004505125604747805 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.758 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.769999999999984 y[1] (analytic) = -12.34308701575714 y[1] (numeric) = -12.34365121137116 absolute error = 0.0005641956140216564 relative error = 0.004570944151178763 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.768 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.779999999999983 y[1] (analytic) = -12.32312963911894 y[1] (numeric) = -12.32370105796956 absolute error = 0.0005714188506242834 relative error = 0.004636962097764137 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.778 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.789999999999983 y[1] (analytic) = -12.30315782416115 y[1] (numeric) = -12.30373646390988 absolute error = 0.0005786397487295147 relative error = 0.004703180736194184 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.788 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799999999999983 y[1] (analytic) = -12.28317157553383 y[1] (numeric) = -12.28375743385327 absolute error = 0.0005858583194413569 relative error = 0.00476960136751892 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.798 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.809999999999983 y[1] (analytic) = -12.26317089786496 y[1] (numeric) = -12.26376397243877 absolute error = 0.0005930745738016441 relative error = 0.004836225302094577 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.808 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.819999999999983 y[1] (analytic) = -12.24315579576059 y[1] (numeric) = -12.24375608428338 absolute error = 0.0006002885227935906 relative error = 0.004903053859703813 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.818 Order of pole (three term test) = 1.527 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.829999999999982 y[1] (analytic) = -12.22312627380494 y[1] (numeric) = -12.22373377398227 absolute error = 0.0006075001773293565 relative error = 0.004970088369546458 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.828 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.839999999999982 y[1] (analytic) = -12.2030823365605 y[1] (numeric) = -12.20369704610879 absolute error = 0.000614709548287351 relative error = 0.005037330170637938 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.838 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.849999999999982 y[1] (analytic) = -12.1830239885682 y[1] (numeric) = -12.18364590521466 absolute error = 0.0006219166464624948 relative error = 0.005104780611497303 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.848 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.859999999999982 y[1] (analytic) = -12.16295123434745 y[1] (numeric) = -12.16358035583007 absolute error = 0.0006291214826195102 relative error = 0.00517244105067945 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.858 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.869999999999981 y[1] (analytic) = -12.14286407839631 y[1] (numeric) = -12.14350040246375 absolute error = 0.0006363240674414072 relative error = 0.005240312856449643 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.868 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.879999999999981 y[1] (analytic) = -12.12276252519158 y[1] (numeric) = -12.12340604960315 absolute error = 0.0006435244115685634 relative error = 0.005308397407202313 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.878 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.889999999999981 y[1] (analytic) = -12.1026465791889 y[1] (numeric) = -12.10329730171449 absolute error = 0.0006507225255880655 relative error = 0.005376696091473207 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.888 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899999999999981 y[1] (analytic) = -12.0825162448229 y[1] (numeric) = -12.08317416324292 absolute error = 0.0006579184200230515 relative error = 0.005445210307951836 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.898 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.909999999999981 y[1] (analytic) = -12.06237152650725 y[1] (numeric) = -12.0630366386126 absolute error = 0.0006651121053504738 relative error = 0.005513941465729851 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.908 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91999999999998 y[1] (analytic) = -12.04221242863482 y[1] (numeric) = -12.0428847322268 absolute error = 0.0006723035919833364 relative error = 0.005582890984257061 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.918 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92999999999998 y[1] (analytic) = -12.02203895557777 y[1] (numeric) = -12.02271844846805 absolute error = 0.0006794928902866815 relative error = 0.005652060293577927 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.928 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93999999999998 y[1] (analytic) = -12.00185111168765 y[1] (numeric) = -12.00253779169822 absolute error = 0.0006866800105687076 relative error = 0.005721450834363412 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.938 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94999999999998 y[1] (analytic) = -11.98164890129553 y[1] (numeric) = -11.98234276625862 absolute error = 0.0006938649630967575 relative error = 0.005791064058150901 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.948 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95999999999998 y[1] (analytic) = -11.96143232871206 y[1] (numeric) = -11.96213337647012 absolute error = 0.0007010477580617902 relative error = 0.005860901427156049 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.958 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.969999999999979 y[1] (analytic) = -11.94120139822763 y[1] (numeric) = -11.94190962663326 absolute error = 0.0007082284056245669 relative error = 0.005930964414767222 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.968 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.979999999999979 y[1] (analytic) = -11.92095611411245 y[1] (numeric) = -11.92167152102833 absolute error = 0.0007154069158747944 relative error = 0.006001254505314974 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.978 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.989999999999979 y[1] (analytic) = -11.90069648061663 y[1] (numeric) = -11.9014190639155 absolute error = 0.0007225832988684289 relative error = 0.006071773194496161 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 4.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.988 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999999999999979 y[1] (analytic) = -11.88042250197033 y[1] (numeric) = -11.88115225953493 absolute error = 0.0007297575645957011 relative error = 0.006142521989219434 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.998 Order of pole (three term test) = 1.528 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 101 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102 %