##############ECHO OF PROBLEM################# ##############temp/sing4_backpostode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=-2.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.05; glob_type_given_pole=2; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=1.0; array_given_ord_poles[1][1]=1.0; 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(1.0 / (x * x + 1.0)); } /* 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 = 2.5e-15 est_needed_step_err = 2.5e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 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 = 2.5e-15 est_needed_step_err = 2.5e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.907347679138423e-222 estimated_step_error = 1.907347679138423e-222 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 500000 step_error = 3.535533905932737e-15 est_needed_step_err = 3.535533905932737e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.310718689280656e-211 estimated_step_error = 1.310718689280656e-211 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 250000 step_error = 5e-15 est_needed_step_err = 5e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.007181240360502e-201 estimated_step_error = 9.007181240360502e-201 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 125000 step_error = 7.071067811865475e-15 est_needed_step_err = 7.071067811865475e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.189675437675637e-190 estimated_step_error = 6.189675437675637e-190 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 62500 step_error = 1e-14 est_needed_step_err = 1e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.253495558411153e-179 estimated_step_error = 4.253495558411153e-179 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 31250 step_error = 1.414213562373095e-14 est_needed_step_err = 1.414213562373095e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.922956506983557e-168 estimated_step_error = 2.922956506983557e-168 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 15625 step_error = 2e-14 est_needed_step_err = 2e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.008608278830409e-157 estimated_step_error = 2.008608278830409e-157 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 7812.5 step_error = 2.82842712474619e-14 est_needed_step_err = 2.82842712474619e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.38026092983183e-146 estimated_step_error = 1.38026092983183e-146 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 3906.25 step_error = 4e-14 est_needed_step_err = 4e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.484473859970062e-136 estimated_step_error = 9.484473859970062e-136 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 1953.125 step_error = 5.65685424949238e-14 est_needed_step_err = 5.65685424949238e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.516846597997249e-125 estimated_step_error = 6.516846597997249e-125 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 976.5625 step_error = 8e-14 est_needed_step_err = 8e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.477196572875267e-114 estimated_step_error = 4.477196572875267e-114 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 488.28125 step_error = 1.131370849898476e-13 est_needed_step_err = 1.131370849898476e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.075131187503782e-103 estimated_step_error = 3.075131187503782e-103 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 244.140625 step_error = 1.6e-13 est_needed_step_err = 1.6e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.111051240003244e-92 estimated_step_error = 2.111051240003244e-92 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.5 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -1 estimated_steps = 122.0703125 step_error = 2.262741699796952e-13 est_needed_step_err = 2.262741699796952e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.44773538009206e-81 estimated_step_error = 1.44773538009206e-81 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.5 y[1] (numeric) = 0.5 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.01 y[1] (analytic) = 0.4950249987624374 y[1] (numeric) = 0.4950249987624375 absolute error = 5.551115123125783e-17 relative error = 1.121380766022639e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.421 Order of pole (given) = 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 = 1.421 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.02 y[1] (analytic) = 0.4900999803960008 y[1] (numeric) = 0.4900999803960008 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.428 Order of pole (given) = 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 = 1.428 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.03 y[1] (analytic) = 0.4852249017419574 y[1] (numeric) = 0.4852249017419574 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.436 Order of pole (given) = 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 = 1.436 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.04 y[1] (analytic) = 0.4803996925441968 y[1] (numeric) = 0.4803996925441967 absolute error = 5.551115123125783e-17 relative error = 1.155520124029863e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.443 Order of pole (given) = 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 = 1.443 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.05 y[1] (analytic) = 0.4756242568370987 y[1] (numeric) = 0.4756242568370986 absolute error = 5.551115123125783e-17 relative error = 1.167121954637196e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 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 = 1.45 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.06 y[1] (analytic) = 0.4708984742889433 y[1] (numeric) = 0.4708984742889433 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 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 = 1.457 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.07 y[1] (analytic) = 0.4662222015012356 y[1] (numeric) = 0.4662222015012354 absolute error = 1.110223024625157e-16 relative error = 2.381317365518498e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 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 = 1.465 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.08 y[1] (analytic) = 0.4615952732644017 y[1] (numeric) = 0.4615952732644018 absolute error = 5.551115123125783e-17 relative error = 1.20259358027397e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.472 Order of pole (given) = 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 = 1.472 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.09 y[1] (analytic) = 0.4570175037703944 y[1] (numeric) = 0.4570175037703944 absolute error = 5.551115123125783e-17 relative error = 1.214639500091153e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.479 Order of pole (given) = 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 = 1.479 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.1 y[1] (analytic) = 0.4524886877828054 y[1] (numeric) = 0.4524886877828054 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.487 Order of pole (given) = 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 = 1.487 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.11 y[1] (analytic) = 0.4480086017651539 y[1] (numeric) = 0.4480086017651539 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.494 Order of pole (given) = 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 = 1.494 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.12 y[1] (analytic) = 0.4435770049680623 y[1] (numeric) = 0.4435770049680625 absolute error = 1.110223024625157e-16 relative error = 2.502886786714954e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.501 Order of pole (given) = 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 = 1.501 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.13 y[1] (analytic) = 0.4391936404760858 y[1] (numeric) = 0.4391936404760859 absolute error = 5.551115123125783e-17 relative error = 1.26393340238451e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.509 Order of pole (given) = 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 = 1.509 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.14 y[1] (analytic) = 0.4348582362149939 y[1] (numeric) = 0.4348582362149939 absolute error = 5.551115123125783e-17 relative error = 1.276534433714005e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.516 Order of pole (given) = 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 = 1.516 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.15 y[1] (analytic) = 0.4305705059203444 y[1] (numeric) = 0.4305705059203445 absolute error = 5.551115123125783e-17 relative error = 1.289246487345963e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.524 Order of pole (given) = 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 = 1.524 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.16 y[1] (analytic) = 0.4263301500682128 y[1] (numeric) = 0.4263301500682128 absolute error = 5.551115123125783e-17 relative error = 1.302069563280384e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.532 Order of pole (given) = 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 = 1.532 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.17 y[1] (analytic) = 0.4221368567689644 y[1] (numeric) = 0.4221368567689645 absolute error = 1.110223024625157e-16 relative error = 2.630007323034534e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.539 Order of pole (given) = 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 = 1.539 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.18 y[1] (analytic) = 0.417990302624979 y[1] (numeric) = 0.4179903026249791 absolute error = 5.551115123125783e-17 relative error = 1.328048782056612e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.547 Order of pole (given) = 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 = 1.547 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.19 y[1] (analytic) = 0.4138901535532469 y[1] (numeric) = 0.413890153553247 absolute error = 5.551115123125783e-17 relative error = 1.34120492489842e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.554 Order of pole (given) = 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 = 1.554 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.2 y[1] (analytic) = 0.4098360655737704 y[1] (numeric) = 0.4098360655737705 absolute error = 5.551115123125783e-17 relative error = 1.354472090042691e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.562 Order of pole (given) = 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 = 1.562 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.21 y[1] (analytic) = 0.4058276855647092 y[1] (numeric) = 0.4058276855647092 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 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 = 1.57 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.22 y[1] (analytic) = 0.4018646519852113 y[1] (numeric) = 0.4018646519852114 absolute error = 5.551115123125783e-17 relative error = 1.38133948723862e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.577 Order of pole (given) = 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 = 1.577 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.23 y[1] (analytic) = 0.3979465955668748 y[1] (numeric) = 0.3979465955668749 absolute error = 5.551115123125783e-17 relative error = 1.394939719290278e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.585 Order of pole (given) = 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 = 1.585 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.24 y[1] (analytic) = 0.3940731399747793 y[1] (numeric) = 0.3940731399747793 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.593 Order of pole (given) = 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 = 1.593 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.25 y[1] (analytic) = 0.3902439024390242 y[1] (numeric) = 0.3902439024390243 absolute error = 1.110223024625157e-16 relative error = 2.844946500601965e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.601 Order of pole (given) = 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 = 1.601 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.26 y[1] (analytic) = 0.3864584943577059 y[1] (numeric) = 0.386458494357706 absolute error = 5.551115123125783e-17 relative error = 1.436406549260028e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.609 Order of pole (given) = 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 = 1.609 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.27 y[1] (analytic) = 0.3827165218722491 y[1] (numeric) = 0.3827165218722492 absolute error = 5.551115123125783e-17 relative error = 1.450450870521536e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.616 Order of pole (given) = 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 = 1.616 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.28 y[1] (analytic) = 0.3790175864160096 y[1] (numeric) = 0.3790175864160097 absolute error = 1.110223024625157e-16 relative error = 2.929212428171014e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.624 Order of pole (given) = 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 = 1.624 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.29 y[1] (analytic) = 0.3753612852370406 y[1] (numeric) = 0.3753612852370407 absolute error = 5.551115123125783e-17 relative error = 1.47887257995194e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.632 Order of pole (given) = 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 = 1.632 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.3 y[1] (analytic) = 0.3717472118959107 y[1] (numeric) = 0.3717472118959108 absolute error = 5.551115123125783e-17 relative error = 1.493249968120836e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 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 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.31 y[1] (analytic) = 0.3681749567394424 y[1] (numeric) = 0.3681749567394426 absolute error = 1.110223024625157e-16 relative error = 3.015476757184388e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.648 Order of pole (given) = 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 = 1.648 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.32 y[1] (analytic) = 0.3646441073512251 y[1] (numeric) = 0.3646441073512252 absolute error = 1.110223024625157e-16 relative error = 3.04467562273203e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.656 Order of pole (given) = 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 = 1.656 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.33 y[1] (analytic) = 0.3611542489797391 y[1] (numeric) = 0.3611542489797392 absolute error = 1.110223024625157e-16 relative error = 3.074096532884597e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.664 Order of pole (given) = 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 = 1.664 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.34 y[1] (analytic) = 0.3577049649449133 y[1] (numeric) = 0.3577049649449134 absolute error = 1.110223024625157e-16 relative error = 3.103739487642088e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.672 Order of pole (given) = 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 = 1.672 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.35 y[1] (analytic) = 0.3542958370239149 y[1] (numeric) = 0.354295837023915 absolute error = 1.110223024625157e-16 relative error = 3.133604487004505e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 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 = 1.68 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.36 y[1] (analytic) = 0.3509264458169567 y[1] (numeric) = 0.3509264458169568 absolute error = 5.551115123125783e-17 relative error = 1.581845765485923e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.688 Order of pole (given) = 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 = 1.688 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.37 y[1] (analytic) = 0.3475963710938857 y[1] (numeric) = 0.3475963710938857 absolute error = 5.551115123125783e-17 relative error = 1.597000309772057e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.696 Order of pole (given) = 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 = 1.696 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.38 y[1] (analytic) = 0.3443051921222971 y[1] (numeric) = 0.3443051921222972 absolute error = 5.551115123125783e-17 relative error = 1.612265876360653e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.704 Order of pole (given) = 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 = 1.704 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.39 y[1] (analytic) = 0.3410524879778997 y[1] (numeric) = 0.3410524879778998 absolute error = 1.110223024625157e-16 relative error = 3.255284930503423e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.712 Order of pole (given) = 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 = 1.712 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (analytic) = 0.3378378378378377 y[1] (numeric) = 0.3378378378378378 absolute error = 1.110223024625157e-16 relative error = 3.286260152890465e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 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 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.41 y[1] (analytic) = 0.3346608212576552 y[1] (numeric) = 0.3346608212576553 absolute error = 1.110223024625157e-16 relative error = 3.317457419882432e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.729 Order of pole (given) = 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 = 1.729 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.42 y[1] (analytic) = 0.3315210184325685 y[1] (numeric) = 0.3315210184325686 absolute error = 5.551115123125783e-17 relative error = 1.674438365739662e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.737 Order of pole (given) = 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 = 1.737 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.43 y[1] (analytic) = 0.3284180104436926 y[1] (numeric) = 0.3284180104436927 absolute error = 5.551115123125783e-17 relative error = 1.69025904384057e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.745 Order of pole (given) = 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 = 1.745 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.44 y[1] (analytic) = 0.3253513794898489 y[1] (numeric) = 0.325351379489849 absolute error = 5.551115123125783e-17 relative error = 1.706190744243941e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.753 Order of pole (given) = 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 = 1.753 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (analytic) = 0.3223207091055599 y[1] (numeric) = 0.32232070910556 absolute error = 1.110223024625157e-16 relative error = 3.44446693389955e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.761 Order of pole (given) = 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 = 1.761 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.46 y[1] (analytic) = 0.3193255843658193 y[1] (numeric) = 0.3193255843658194 absolute error = 1.110223024625157e-16 relative error = 3.476774423916142e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 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 = 1.77 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.47 y[1] (analytic) = 0.3163655920782055 y[1] (numeric) = 0.3163655920782056 absolute error = 1.110223024625157e-16 relative error = 3.509303958537658e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.778 Order of pole (given) = 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 = 1.778 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.48 y[1] (analytic) = 0.3134403209628885 y[1] (numeric) = 0.3134403209628887 absolute error = 1.110223024625157e-16 relative error = 3.542055537764101e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.786 Order of pole (given) = 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 = 1.786 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.49 y[1] (analytic) = 0.3105493618210614 y[1] (numeric) = 0.3105493618210615 absolute error = 1.110223024625157e-16 relative error = 3.575029161595468e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.794 Order of pole (given) = 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 = 1.794 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 0.3076923076923075 y[1] (numeric) = 0.3076923076923077 absolute error = 1.665334536937735e-16 relative error = 5.412337245047641e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.803 Order of pole (given) = 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 = 1.803 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 0.3048687540014023 y[1] (numeric) = 0.3048687540014024 absolute error = 1.110223024625157e-16 relative error = 3.641642543072977e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.811 Order of pole (given) = 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 = 1.811 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 0.3020782986950216 y[1] (numeric) = 0.3020782986950217 absolute error = 1.110223024625157e-16 relative error = 3.67528230071912e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.819 Order of pole (given) = 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 = 1.819 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 0.2993205423688227 y[1] (numeric) = 0.2993205423688228 absolute error = 1.110223024625157e-16 relative error = 3.709144102970187e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.828 Order of pole (given) = 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 = 1.828 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 0.2965950883853362 y[1] (numeric) = 0.2965950883853363 absolute error = 1.110223024625157e-16 relative error = 3.743227949826179e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 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 = 1.836 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = 0.2939015429831005 y[1] (numeric) = 0.2939015429831007 absolute error = 1.665334536937735e-16 relative error = 5.666300761930646e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 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 = 1.845 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = 0.2912395153774463 y[1] (numeric) = 0.2912395153774464 absolute error = 1.110223024625157e-16 relative error = 3.812061777352939e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 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 = 1.853 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.570000000000001 y[1] (analytic) = 0.288608617853329 y[1] (numeric) = 0.2886086178533291 absolute error = 1.110223024625157e-16 relative error = 3.846811758023706e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.861 Order of pole (given) = 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 = 1.861 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.580000000000001 y[1] (analytic) = 0.286008465850589 y[1] (numeric) = 0.2860084658505891 absolute error = 1.110223024625157e-16 relative error = 3.881783783299399e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 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 = 1.87 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.590000000000001 y[1] (analytic) = 0.2834386780420055 y[1] (numeric) = 0.2834386780420056 absolute error = 5.551115123125783e-17 relative error = 1.958488926590008e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 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 = 1.878 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.600000000000001 y[1] (analytic) = 0.2808988764044942 y[1] (numeric) = 0.2808988764044943 absolute error = 1.110223024625157e-16 relative error = 3.952393967665559e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 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 = 1.887 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.610000000000001 y[1] (analytic) = 0.2783886862837893 y[1] (numeric) = 0.2783886862837894 absolute error = 5.551115123125783e-17 relative error = 1.994016063378013e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 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 = 1.895 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.620000000000001 y[1] (analytic) = 0.27590773645293 y[1] (numeric) = 0.2759077364529301 absolute error = 1.110223024625157e-16 relative error = 4.02389233045142e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.904 Order of pole (given) = 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 = 1.904 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.630000000000001 y[1] (analytic) = 0.2734556591648662 y[1] (numeric) = 0.2734556591648664 absolute error = 1.110223024625157e-16 relative error = 4.059974578751737e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 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 = 1.912 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.640000000000001 y[1] (analytic) = 0.2710320901994795 y[1] (numeric) = 0.2710320901994795 absolute error = 5.551115123125783e-17 relative error = 2.04813943582849e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.921 Order of pole (given) = 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 = 1.921 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.650000000000001 y[1] (analytic) = 0.2686366689053054 y[1] (numeric) = 0.2686366689053055 absolute error = 1.110223024625157e-16 relative error = 4.132805209167148e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.929 Order of pole (given) = 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 = 1.929 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.660000000000001 y[1] (analytic) = 0.2662690382362338 y[1] (numeric) = 0.2662690382362338 absolute error = 5.551115123125783e-17 relative error = 2.08477679564112e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.938 Order of pole (given) = 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 = 1.938 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.670000000000001 y[1] (analytic) = 0.2639288447834462 y[1] (numeric) = 0.2639288447834463 absolute error = 5.551115123125783e-17 relative error = 2.103262009001129e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 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 = 1.947 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.680000000000001 y[1] (analytic) = 0.2616157388028462 y[1] (numeric) = 0.2616157388028463 absolute error = 5.551115123125783e-17 relative error = 2.1218582446636e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 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 = 1.955 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.690000000000001 y[1] (analytic) = 0.2593293742382198 y[1] (numeric) = 0.2593293742382198 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.964 Order of pole (given) = 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 = 1.964 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.700000000000001 y[1] (analytic) = 0.2570694087403598 y[1] (numeric) = 0.2570694087403598 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 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 = 1.972 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.710000000000001 y[1] (analytic) = 0.2548355036823729 y[1] (numeric) = 0.2548355036823729 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.981 Order of pole (given) = 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 = 1.981 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.720000000000001 y[1] (analytic) = 0.2526273241713822 y[1] (numeric) = 0.2526273241713822 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 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 = 1.99 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.730000000000001 y[1] (analytic) = 0.2504445390568257 y[1] (numeric) = 0.2504445390568257 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 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 = 1.998 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.740000000000001 y[1] (analytic) = 0.2482868209355446 y[1] (numeric) = 0.2482868209355446 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.007 Order of pole (given) = 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 = 2.007 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.750000000000001 y[1] (analytic) = 0.2461538461538461 y[1] (numeric) = 0.246153846153846 absolute error = 2.775557561562891e-17 relative error = 1.127570259384925e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 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 = 2.016 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.760000000000001 y[1] (analytic) = 0.244045294806716 y[1] (numeric) = 0.244045294806716 absolute error = 2.775557561562891e-17 relative error = 1.137312466426011e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.024 Order of pole (given) = 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 = 2.024 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.770000000000001 y[1] (analytic) = 0.241960850734351 y[1] (numeric) = 0.2419608507343511 absolute error = 5.551115123125783e-17 relative error = 2.294220369236656e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.033 Order of pole (given) = 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 = 2.033 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.780000000000001 y[1] (analytic) = 0.2399002015161692 y[1] (numeric) = 0.2399002015161691 absolute error = 2.775557561562891e-17 relative error = 1.156963413961876e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.042 Order of pole (given) = 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 = 2.042 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.790000000000001 y[1] (analytic) = 0.2378630384624532 y[1] (numeric) = 0.2378630384624532 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 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 = 2.05 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.800000000000001 y[1] (analytic) = 0.2358490566037735 y[1] (numeric) = 0.2358490566037734 absolute error = 2.775557561562891e-17 relative error = 1.176836406102666e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 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 = 2.059 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.810000000000001 y[1] (analytic) = 0.2338579546783282 y[1] (numeric) = 0.2338579546783283 absolute error = 5.551115123125783e-17 relative error = 2.373712337799818e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 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 = 2.068 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.820000000000001 y[1] (analytic) = 0.231889435117336 y[1] (numeric) = 0.2318894351173359 absolute error = 2.775557561562891e-17 relative error = 1.196931442848382e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 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 = 2.077 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.830000000000001 y[1] (analytic) = 0.2299432040286048 y[1] (numeric) = 0.2299432040286048 absolute error = 2.775557561562891e-17 relative error = 1.207062227948086e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 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 = 2.085 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.840000000000001 y[1] (analytic) = 0.2280189711784019 y[1] (numeric) = 0.2280189711784019 absolute error = 2.775557561562891e-17 relative error = 1.217248524199022e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 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 = 2.094 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.850000000000001 y[1] (analytic) = 0.2261164499717353 y[1] (numeric) = 0.2261164499717353 absolute error = 2.775557561562891e-17 relative error = 1.227490331601189e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 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 = 2.103 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.860000000000001 y[1] (analytic) = 0.2242353574311596 y[1] (numeric) = 0.2242353574311596 absolute error = 2.775557561562891e-17 relative error = 1.237787650154588e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 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 = 2.112 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.870000000000001 y[1] (analytic) = 0.2223754141742088 y[1] (numeric) = 0.2223754141742088 absolute error = 2.775557561562891e-17 relative error = 1.248140479859217e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.121 Order of pole (given) = 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 = 2.121 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.880000000000001 y[1] (analytic) = 0.2205363443895552 y[1] (numeric) = 0.2205363443895553 absolute error = 2.775557561562891e-17 relative error = 1.258548820715078e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 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 = 2.129 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.890000000000001 y[1] (analytic) = 0.21871787581199 y[1] (numeric) = 0.21871787581199 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 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 = 2.138 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.900000000000001 y[1] (analytic) = 0.2169197396963122 y[1] (numeric) = 0.2169197396963122 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 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 = 2.147 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.910000000000001 y[1] (analytic) = 0.2151416707902152 y[1] (numeric) = 0.2151416707902152 absolute error = 2.775557561562891e-17 relative error = 1.290106910190048e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.156 Order of pole (given) = 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 = 2.156 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.920000000000001 y[1] (analytic) = 0.2133834073062477 y[1] (numeric) = 0.2133834073062477 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.165 Order of pole (given) = 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 = 2.165 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.930000000000001 y[1] (analytic) = 0.2116446908929288 y[1] (numeric) = 0.2116446908929288 absolute error = 2.775557561562891e-17 relative error = 1.311423192262851e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 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 = 2.174 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.940000000000001 y[1] (analytic) = 0.2099252666050884 y[1] (numeric) = 0.2099252666050885 absolute error = 5.551115123125783e-17 relative error = 2.6443292000522e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 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 = 2.183 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.950000000000001 y[1] (analytic) = 0.2082248828735032 y[1] (numeric) = 0.2082248828735033 absolute error = 5.551115123125783e-17 relative error = 2.665923037881159e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 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 = 2.191 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.960000000000001 y[1] (analytic) = 0.2065432914738928 y[1] (numeric) = 0.2065432914738928 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 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 = 2.2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.970000000000001 y[1] (analytic) = 0.2048802474953388 y[1] (numeric) = 0.2048802474953388 absolute error = 2.775557561562891e-17 relative error = 1.354721890223233e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 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 = 2.209 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.980000000000001 y[1] (analytic) = 0.2032355093081862 y[1] (numeric) = 0.2032355093081862 absolute error = 2.775557561562891e-17 relative error = 1.365685342591406e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.218 Order of pole (given) = 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 = 2.218 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.990000000000001 y[1] (analytic) = 0.2016088385314811 y[1] (numeric) = 0.2016088385314811 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = -0.01 Radius of convergence (given) for eq 1 = 2.227 Order of pole (given) = 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 = 2.227 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; Iterations = 100 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 0 %