##############ECHO OF PROBLEM################# ##############temp/sing2postode.ode################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=16; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-2.0; x_end=-1.5; 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=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // 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 = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 500000 step_error = 7.071067811865475e-21 est_needed_step_err = 7.071067811865475e-21 opt_iter = 1 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 500000 step_error = 7.828723661341925e-21 est_needed_step_err = 7.828723661341925e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.450574160593344e-103 estimated_step_error = 1.450574160593344e-103 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 250000 step_error = 1.10714871779409e-20 est_needed_step_err = 1.10714871779409e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.506485024763502e-99 estimated_step_error = 9.506485024763502e-99 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 125000 step_error = 1.565744732268385e-20 est_needed_step_err = 1.565744732268385e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.230172917146513e-94 estimated_step_error = 6.230172917146513e-94 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 62500 step_error = 2.21429743558818e-20 est_needed_step_err = 2.21429743558818e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.083009912693051e-89 estimated_step_error = 4.083009912693051e-89 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 31250 step_error = 3.13148946453677e-20 est_needed_step_err = 3.13148946453677e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.675846343644817e-84 estimated_step_error = 2.675846343644817e-84 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 15625 step_error = 4.428594871176361e-20 est_needed_step_err = 4.428594871176361e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.75364917049021e-79 estimated_step_error = 1.75364917049021e-79 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 7812.5 step_error = 6.26297892907354e-20 est_needed_step_err = 6.26297892907354e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.149280054178546e-74 estimated_step_error = 1.149280054178546e-74 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 3906.25 step_error = 8.857189742352722e-20 est_needed_step_err = 8.857189742352722e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.532033619367497e-70 estimated_step_error = 7.532033619367497e-70 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 1953.125 step_error = 1.252595785814708e-19 est_needed_step_err = 1.252595785814708e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.93634017032486e-65 estimated_step_error = 4.93634017032486e-65 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 976.5625 step_error = 1.771437948470544e-19 est_needed_step_err = 1.771437948470544e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.235272082305514e-60 estimated_step_error = 3.235272082305514e-60 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 488.28125 step_error = 2.505191571629416e-19 est_needed_step_err = 2.505191571629416e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.120519852918538e-55 estimated_step_error = 2.120519852918538e-55 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 244.140625 step_error = 3.542875896941089e-19 est_needed_step_err = 3.542875896941089e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.390034209479254e-50 estimated_step_error = 1.390034209479254e-50 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 122.0703125 step_error = 5.010383143258832e-19 est_needed_step_err = 5.010383143258832e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.114060226246165e-46 estimated_step_error = 9.114060226246165e-46 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 61.03515625 step_error = 7.085751793882178e-19 est_needed_step_err = 7.085751793882178e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.978675092256558e-41 estimated_step_error = 5.978675092256558e-41 Double H and LOOP opt_iter = 15 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 30.517578125 step_error = 1.002076628651766e-18 est_needed_step_err = 1.002076628651766e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.925652484578803e-36 estimated_step_error = 3.925652484578803e-36 Double H and LOOP opt_iter = 16 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -2.576e-14 min_size = 1.10714871779409 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1.10714871779409 desired_abs_gbl_error = 1.10714871779409e-16 range = 0.5 estimated_steps = 15.2587890625 step_error = 1.417150358776436e-18 est_needed_step_err = 1.417150358776436e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.582548990324446e-31 estimated_step_error = 2.582548990324446e-31 Double H and LOOP opt_iter = 17 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 2.236 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 = 1.706 Order of pole (six term test) = -2.576e-14 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (closed_form) = -1.10714871779409 y[1] (numeric) = -1.10714871779409 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.236 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 = 2.236 Order of pole (six term test) = -1.155e-14 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (closed_form) = -1.096944990300136 y[1] (numeric) = -1.096944990300136 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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) = -2.141e-13 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = -1.086318397757873 y[1] (numeric) = -1.086318397757873 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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) = -1.332e-14 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (closed_form) = -1.075244653309068 y[1] (numeric) = -1.075244653309068 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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) = -3.642e-14 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (closed_form) = -1.06369782240256 y[1] (numeric) = -1.06369782240256 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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) = -6.661e-14 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (closed_form) = -1.051650212548374 y[1] (numeric) = -1.051650212548374 absolute error = 2.220446049250313e-16 relative error = 2.111392193674071e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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) = -2.132e-14 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (closed_form) = -1.039072259536091 y[1] (numeric) = -1.039072259536091 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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) = 1.155e-14 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (closed_form) = -1.025932411343353 y[1] (numeric) = -1.025932411343353 absolute error = 2.220446049250313e-16 relative error = 2.164320012409851e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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) = 1.599e-14 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (closed_form) = -1.012197011451334 y[1] (numeric) = -1.012197011451334 absolute error = 2.220446049250313e-16 relative error = 2.193689592173896e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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) = 7.105e-15 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (closed_form) = -0.9978301839061904 y[1] (numeric) = -0.9978301839061906 absolute error = 2.220446049250313e-16 relative error = 2.225274485642404e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05 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) = -8.882e-15 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 110 %