##############ECHO OF PROBLEM################# ##############temp/sing2_backpostode.ode################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.5; x_end=-2.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; 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(arctan(x)); } /* 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 = -0.5 estimated_steps = 500000 step_error = 7.071067811865475e-15 est_needed_step_err = 7.071067811865475e-15 opt_iter = 1 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 500000 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 = 8.40342006704583e-104 estimated_step_error = 8.40342006704583e-104 Double H and LOOP opt_iter = 2 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 250000 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 = 5.507311820934126e-99 estimated_step_error = 5.507311820934126e-99 Double H and LOOP opt_iter = 3 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 125000 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 = 3.609332752318682e-94 estimated_step_error = 3.609332752318682e-94 Double H and LOOP opt_iter = 4 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 62500 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 = 2.36549210550889e-89 estimated_step_error = 2.36549210550889e-89 Double H and LOOP opt_iter = 5 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 31250 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 = 1.550353491923595e-84 estimated_step_error = 1.550353491923595e-84 Double H and LOOP opt_iter = 6 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 15625 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 = 1.016176745519009e-79 estimated_step_error = 1.016176745519009e-79 Double H and LOOP opt_iter = 7 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 7812.5 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 = 6.661412629905312e-75 estimated_step_error = 6.661412629905312e-75 Double H and LOOP opt_iter = 8 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 3906.25 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 = 4.367978265106604e-70 estimated_step_error = 4.367978265106604e-70 Double H and LOOP opt_iter = 9 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 1953.125 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 = 2.865684566221823e-65 estimated_step_error = 2.865684566221823e-65 Double H and LOOP opt_iter = 10 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 976.5625 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 = 1.882099662642142e-60 estimated_step_error = 1.882099662642142e-60 Double H and LOOP opt_iter = 11 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 488.28125 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 = 1.238752398765103e-55 estimated_step_error = 1.238752398765103e-55 Double H and LOOP opt_iter = 12 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 244.140625 step_error = 3.2e-13 est_needed_step_err = 3.2e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.187702806745811e-51 estimated_step_error = 8.187702806745811e-51 Double H and LOOP opt_iter = 13 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 122.0703125 step_error = 4.525483399593904e-13 est_needed_step_err = 4.525483399593904e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.456752634924327e-46 estimated_step_error = 5.456752634924327e-46 Double H and LOOP opt_iter = 14 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) = -4.441e-15 min_size = 0.9827937232473291 min_size = 1 glob_desired_digits_correct = 10 estimated_h = -0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = -0.5 estimated_steps = 61.03515625 step_error = 6.4e-13 est_needed_step_err = 6.4e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.694904616149563e-41 estimated_step_error = 3.694904616149563e-41 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL 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 = 1.1 Order of pole (six term test) = -4.441e-15 START of Soultion TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = -0.9827937232473291 y[1] (numeric) = -0.9827937232473291 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 = 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) = 7.994e-14 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = -0.9858565008066836 y[1] (numeric) = -0.9858565008066835 absolute error = 1.110223024625157e-16 relative error = 1.126150736660669e-14 % Desired digits = 10 Estimated correct digits = 13 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) = 5.063e-14 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = -0.9888912086550111 y[1] (numeric) = -0.988891208655011 absolute error = 1.110223024625157e-16 relative error = 1.12269480698e-14 % Desired digits = 10 Estimated correct digits = 13 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) = 2.753e-14 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = -0.9918981757768771 y[1] (numeric) = -0.991898175776877 absolute error = 1.110223024625157e-16 relative error = 1.119291326204532e-14 % Desired digits = 10 Estimated correct digits = 13 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) = 1.155e-14 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = -0.9948777271765435 y[1] (numeric) = -0.9948777271765434 absolute error = 1.110223024625157e-16 relative error = 1.115939169505746e-14 % Desired digits = 10 Estimated correct digits = 13 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) = -3.286e-14 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = -0.9978301839061905 y[1] (numeric) = -0.9978301839061903 absolute error = 2.220446049250313e-16 relative error = 2.225274485642404e-14 % Desired digits = 10 Estimated correct digits = 12 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) = 1.954e-14 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = -1.000755863095186 y[1] (numeric) = -1.000755863095186 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 = 1.853 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) = 3.642e-14 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = -1.003655077980327 y[1] (numeric) = -1.003655077980327 absolute error = 2.220446049250313e-16 relative error = 2.212359702018901e-14 % Desired digits = 10 Estimated correct digits = 12 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) = 8.882e-15 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = -1.006528137936965 y[1] (numeric) = -1.006528137936965 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 = 1.87 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) = -5.329e-15 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = -1.009375348510952 y[1] (numeric) = -1.009375348510952 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 = 1.878 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) = 9.77e-15 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = -1.012197011451334 y[1] (numeric) = -1.012197011451334 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 = 1.887 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) = 2.665e-14 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = -1.014993424743717 y[1] (numeric) = -1.014993424743717 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 = 1.895 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) = 3.109e-14 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = -1.017764882644256 y[1] (numeric) = -1.017764882644256 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 = 1.904 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) = -6.217e-15 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = -1.020511675714193 y[1] (numeric) = -1.020511675714193 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 = 1.912 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) = 7.994e-15 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = -1.023234090854899 y[1] (numeric) = -1.023234090854899 absolute error = 2.220446049250313e-16 relative error = 2.17002743467544e-14 % Desired digits = 10 Estimated correct digits = 12 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) = 4.441e-15 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = -1.025932411343353 y[1] (numeric) = -1.025932411343353 absolute error = 2.220446049250313e-16 relative error = 2.16432001240985e-14 % Desired digits = 10 Estimated correct digits = 12 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) = 5.329e-15 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = -1.028606916868018 y[1] (numeric) = -1.028606916868018 absolute error = 2.220446049250313e-16 relative error = 2.158692512015473e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.421e-14 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = -1.031257883565058 y[1] (numeric) = -1.031257883565058 absolute error = 2.220446049250313e-16 relative error = 2.153143345265136e-14 % Desired digits = 10 Estimated correct digits = 12 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) = 1.155e-14 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = -1.033885584054851 y[1] (numeric) = -1.033885584054851 absolute error = 2.220446049250313e-16 relative error = 2.147670964268432e-14 % Desired digits = 10 Estimated correct digits = 12 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) = 0 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = -1.036490287478756 y[1] (numeric) = -1.036490287478756 absolute error = 2.220446049250313e-16 relative error = 2.142273860232215e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.776e-15 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = -1.039072259536091 y[1] (numeric) = -1.039072259536091 absolute error = 2.220446049250313e-16 relative error = 2.136950562265673e-14 % Desired digits = 10 Estimated correct digits = 12 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) = 6.217e-15 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = -1.041631762521281 y[1] (numeric) = -1.041631762521281 absolute error = 2.220446049250313e-16 relative error = 2.13169963622816e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -2.132e-14 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = -1.044169055361146 y[1] (numeric) = -1.044169055361146 absolute error = 2.220446049250313e-16 relative error = 2.126519683618022e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.51e-14 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = -1.046684393652281 y[1] (numeric) = -1.04668439365228 absolute error = 2.220446049250313e-16 relative error = 2.121409340500751e-14 % Desired digits = 10 Estimated correct digits = 12 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) = 0 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = -1.04917802969851 y[1] (numeric) = -1.04917802969851 absolute error = 2.220446049250313e-16 relative error = 2.116367276474877e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -2.665e-15 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = -1.051650212548374 y[1] (numeric) = -1.051650212548373 absolute error = 4.440892098500626e-16 relative error = 4.222784387348141e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -5.684e-14 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = -1.054101188032619 y[1] (numeric) = -1.054101188032619 absolute error = 4.440892098500626e-16 relative error = 4.212965651608014e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -9.77e-15 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = -1.056531198801675 y[1] (numeric) = -1.056531198801675 absolute error = 4.440892098500626e-16 relative error = 4.20327587442521e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -3.02e-14 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = -1.058940484363073 y[1] (numeric) = -1.058940484363072 absolute error = 4.440892098500626e-16 relative error = 4.193712643984631e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -7.994e-15 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = -1.0613292811188 y[1] (numeric) = -1.0613292811188 absolute error = 4.440892098500626e-16 relative error = 4.184273606226393e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -2.842e-14 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = -1.06369782240256 y[1] (numeric) = -1.063697822402559 absolute error = 4.440892098500626e-16 relative error = 4.174956463171133e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -7.105e-15 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = -1.066046338516909 y[1] (numeric) = -1.066046338516909 absolute error = 4.440892098500626e-16 relative error = 4.165758971302153e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.688e-14 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = -1.068375056770266 y[1] (numeric) = -1.068375056770265 absolute error = 4.440892098500626e-16 relative error = 4.156678940002207e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -5.507e-14 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = -1.070684201513757 y[1] (numeric) = -1.070684201513757 absolute error = 4.440892098500626e-16 relative error = 4.147714230042803e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.332e-14 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = -1.072973994177896 y[1] (numeric) = -1.072973994177895 absolute error = 4.440892098500626e-16 relative error = 4.138862752124019e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -5.063e-14 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = -1.075244653309068 y[1] (numeric) = -1.075244653309068 absolute error = 2.220446049250313e-16 relative error = 2.065061232731439e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -2.309e-14 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = -1.077496394605818 y[1] (numeric) = -1.077496394605817 absolute error = 4.440892098500626e-16 relative error = 4.121491376428452e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.421e-14 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = -1.079729430954907 y[1] (numeric) = -1.079729430954906 absolute error = 2.220446049250313e-16 relative error = 2.056483768610959e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.865e-14 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = -1.081943972467149 y[1] (numeric) = -1.081943972467149 absolute error = 2.220446049250313e-16 relative error = 2.052274522299936e-14 % Desired digits = 10 Estimated correct digits = 12 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) = 0 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = -1.084140226512997 y[1] (numeric) = -1.084140226512997 absolute error = 2.220446049250313e-16 relative error = 2.048117019319635e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -5.24e-14 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = -1.086318397757873 y[1] (numeric) = -1.086318397757873 absolute error = 2.220446049250313e-16 relative error = 2.044010350771231e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -7.105e-15 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = -1.088478688197237 y[1] (numeric) = -1.088478688197236 absolute error = 4.440892098500626e-16 relative error = 4.079907256480816e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -4.174e-14 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = -1.09062129719137 y[1] (numeric) = -1.090621297191369 absolute error = 4.440892098500626e-16 relative error = 4.071891966475499e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -9.681e-14 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = -1.092746421499885 y[1] (numeric) = -1.092746421499885 absolute error = 4.440892098500626e-16 relative error = 4.06397313331407e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -7.727e-14 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = -1.094854255315938 y[1] (numeric) = -1.094854255315938 absolute error = 4.440892098500626e-16 relative error = 4.056149096501555e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.164e-13 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = -1.096944990300136 y[1] (numeric) = -1.096944990300136 absolute error = 4.440892098500626e-16 relative error = 4.048418232244763e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -7.372e-14 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = -1.099018815614147 y[1] (numeric) = -1.099018815614146 absolute error = 6.661338147750939e-16 relative error = 6.061168428702918e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.181e-13 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = -1.101075917953986 y[1] (numeric) = -1.101075917953986 absolute error = 6.661338147750939e-16 relative error = 6.049844555795029e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.021e-13 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = -1.103116481582997 y[1] (numeric) = -1.103116481582996 absolute error = 8.881784197001252e-16 relative error = 8.05153793392307e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -1.297e-13 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = -1.105140688364494 y[1] (numeric) = -1.105140688364494 absolute error = 6.661338147750939e-16 relative error = 6.02759288286553e-14 % Desired digits = 10 Estimated correct digits = 12 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) = -8.082e-14 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; Iterations = 50 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 %