##############ECHO OF PROBLEM################# ##############temp/div_c_linpostode.ode################# diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=2.5; x_end=3.1; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; array_given_rad_poles[1][2]=0.0; 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(10.0* ln(0.2* x + 0.3)); } /* 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 = 0.6000000000000001 estimated_steps = 600000.0000000001 step_error = 4.303314829119352e-15 est_needed_step_err = 4.303314829119352e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 600000.0000000001 step_error = 9.602569533927935e-15 est_needed_step_err = 9.602569533927935e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 300000.0000000001 step_error = 1.358008406851158e-14 est_needed_step_err = 1.358008406851158e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 150000 step_error = 1.920513906785587e-14 est_needed_step_err = 1.920513906785587e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 75000.00000000001 step_error = 2.716016813702316e-14 est_needed_step_err = 2.716016813702316e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 37500.00000000001 step_error = 3.841027813571174e-14 est_needed_step_err = 3.841027813571174e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 18750 step_error = 5.432033627404631e-14 est_needed_step_err = 5.432033627404631e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 9375.000000000002 step_error = 7.682055627142348e-14 est_needed_step_err = 7.682055627142348e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 4687.500000000001 step_error = 1.086406725480926e-13 est_needed_step_err = 1.086406725480926e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 2343.75 step_error = 1.53641112542847e-13 est_needed_step_err = 1.53641112542847e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 1171.875 step_error = 2.172813450961853e-13 est_needed_step_err = 2.172813450961853e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 585.9375000000001 step_error = 3.072822250856939e-13 est_needed_step_err = 3.072822250856939e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 292.9687500000001 step_error = 4.345626901923705e-13 est_needed_step_err = 4.345626901923705e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 146.484375 step_error = 6.145644501713878e-13 est_needed_step_err = 6.145644501713878e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 4 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 = 2.231435513142097 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 2.231435513142097 desired_abs_gbl_error = 2.231435513142097e-10 range = 0.6000000000000001 estimated_steps = 73.24218750000001 step_error = 8.69125380384741e-13 est_needed_step_err = 8.69125380384741e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 4 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] = 2.5 y[1] (analytic) = -2.231435513142097 y[1] (numeric) = -2.231435513142097 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 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] = 2.51 y[1] (analytic) = -2.206466711156225 y[1] (numeric) = -2.206466711156225 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 4.01 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] = 2.52 y[1] (analytic) = -2.181560098031709 y[1] (numeric) = -2.181560098031706 absolute error = 3.552713678800501e-15 relative error = 1.628519737781188e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.02 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] = 2.529999999999999 y[1] (analytic) = -2.156715364755089 y[1] (numeric) = -2.156715364755086 absolute error = 3.552713678800501e-15 relative error = 1.647279811169675e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.03 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] = 2.539999999999999 y[1] (analytic) = -2.131932204610419 y[1] (numeric) = -2.131932204610415 absolute error = 3.996802888650564e-15 relative error = 1.874732639249626e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.04 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] = 2.549999999999999 y[1] (analytic) = -2.107210313156528 y[1] (numeric) = -2.107210313156524 absolute error = 4.440892098500626e-15 relative error = 2.107474546215714e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.05 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] = 2.559999999999999 y[1] (analytic) = -2.082549388204593 y[1] (numeric) = -2.082549388204588 absolute error = 4.884981308350689e-15 relative error = 2.345673690150574e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.06 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] = 2.569999999999999 y[1] (analytic) = -2.057949129795972 y[1] (numeric) = -2.057949129795964 absolute error = 7.993605777301127e-15 relative error = 3.884258197428633e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.07 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] = 2.579999999999998 y[1] (analytic) = -2.033409240180305 y[1] (numeric) = -2.033409240180297 absolute error = 8.43769498715119e-15 relative error = 4.149531152127059e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.08 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] = 2.589999999999998 y[1] (analytic) = -2.008929423793905 y[1] (numeric) = -2.008929423793896 absolute error = 8.43769498715119e-15 relative error = 4.200095278218599e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.09 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] = 2.599999999999998 y[1] (analytic) = -1.984509387238387 y[1] (numeric) = -1.984509387238378 absolute error = 8.881784197001252e-15 relative error = 4.475556656026207e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.1 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] = 2.609999999999998 y[1] (analytic) = -1.960148839259576 y[1] (numeric) = -1.960148839259567 absolute error = 9.103828801926284e-15 relative error = 4.644457920534827e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.11 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] = 2.619999999999997 y[1] (analytic) = -1.935847490726661 y[1] (numeric) = -1.935847490726649 absolute error = 1.221245327087672e-14 relative error = 6.308582328607158e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.12 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] = 2.629999999999997 y[1] (analytic) = -1.911605054611597 y[1] (numeric) = -1.911605054611585 absolute error = 1.243449787580175e-14 relative error = 6.504742099213697e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.13 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] = 2.639999999999997 y[1] (analytic) = -1.887421245968781 y[1] (numeric) = -1.887421245968768 absolute error = 1.287858708565182e-14 relative error = 6.823377194231729e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.14 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] = 2.649999999999997 y[1] (analytic) = -1.863295781914942 y[1] (numeric) = -1.863295781914929 absolute error = 1.310063169057685e-14 relative error = 7.030892152352268e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.15 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] = 2.659999999999997 y[1] (analytic) = -1.839228381609292 y[1] (numeric) = -1.839228381609278 absolute error = 1.332267629550188e-14 relative error = 7.243622613002947e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.16 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] = 2.669999999999996 y[1] (analytic) = -1.815218766233913 y[1] (numeric) = -1.815218766233896 absolute error = 1.643130076445232e-14 relative error = 9.0519672174516e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.17 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] = 2.679999999999996 y[1] (analytic) = -1.791266658974364 y[1] (numeric) = -1.791266658974347 absolute error = 1.665334536937735e-14 relative error = 9.296966080367202e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.18 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] = 2.689999999999996 y[1] (analytic) = -1.76737178500055 y[1] (numeric) = -1.767371785000533 absolute error = 1.687538997430238e-14 relative error = 9.548296582259363e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.19 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] = 2.699999999999996 y[1] (analytic) = -1.743533871447787 y[1] (numeric) = -1.74353387144777 absolute error = 1.709743457922741e-14 relative error = 9.806195829754732e-13 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 4.2 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] = 2.709999999999996 y[1] (analytic) = -1.719752647398113 y[1] (numeric) = -1.719752647398095 absolute error = 1.754152378907747e-14 relative error = 1.020002720485227e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.21 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] = 2.719999999999995 y[1] (analytic) = -1.696027843861811 y[1] (numeric) = -1.696027843861791 absolute error = 2.042810365310288e-14 relative error = 1.204467469507377e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.22 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] = 2.729999999999995 y[1] (analytic) = -1.67235919375915 y[1] (numeric) = -1.672359193759129 absolute error = 2.065014825802791e-14 relative error = 1.234791445228357e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.23 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] = 2.739999999999995 y[1] (analytic) = -1.648746431902352 y[1] (numeric) = -1.648746431902331 absolute error = 2.087219286295294e-14 relative error = 1.265943171071506e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.24 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] = 2.749999999999995 y[1] (analytic) = -1.625189294977761 y[1] (numeric) = -1.62518929497774 absolute error = 2.131628207280301e-14 relative error = 1.3116184150779e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.25 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] = 2.759999999999994 y[1] (analytic) = -1.601687521528225 y[1] (numeric) = -1.601687521528204 absolute error = 2.176037128265307e-14 relative error = 1.358590298680154e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.26 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] = 2.769999999999994 y[1] (analytic) = -1.578240851935686 y[1] (numeric) = -1.578240851935662 absolute error = 2.442490654175344e-14 relative error = 1.547603238871729e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.27 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] = 2.779999999999994 y[1] (analytic) = -1.554849028403964 y[1] (numeric) = -1.554849028403939 absolute error = 2.486899575160351e-14 relative error = 1.59944761821225e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.28 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] = 2.789999999999994 y[1] (analytic) = -1.531511794941762 y[1] (numeric) = -1.531511794941737 absolute error = 2.509104035652854e-14 relative error = 1.638318453661185e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.29 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] = 2.799999999999994 y[1] (analytic) = -1.508228897345851 y[1] (numeric) = -1.508228897345825 absolute error = 2.55351295663786e-14 relative error = 1.693053992753671e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.3 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] = 2.809999999999993 y[1] (analytic) = -1.485000083184454 y[1] (numeric) = -1.485000083184428 absolute error = 2.55351295663786e-14 relative error = 1.719537248214878e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.31 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] = 2.819999999999993 y[1] (analytic) = -1.461825101780831 y[1] (numeric) = -1.461825101780803 absolute error = 2.842170943040401e-14 relative error = 1.944261963745183e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.32 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] = 2.829999999999993 y[1] (analytic) = -1.438703704197036 y[1] (numeric) = -1.438703704197007 absolute error = 2.842170943040401e-14 relative error = 1.975508184728462e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.33 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] = 2.839999999999993 y[1] (analytic) = -1.415635643217885 y[1] (numeric) = -1.415635643217857 absolute error = 2.864375403532904e-14 relative error = 2.023384630964705e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.34 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] = 2.849999999999993 y[1] (analytic) = -1.392620673335093 y[1] (numeric) = -1.392620673335064 absolute error = 2.90878432451791e-14 relative error = 2.088712583557918e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.35 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] = 2.859999999999992 y[1] (analytic) = -1.369658550731591 y[1] (numeric) = -1.369658550731562 absolute error = 2.930988785010413e-14 relative error = 2.13994121633078e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.36 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] = 2.869999999999992 y[1] (analytic) = -1.346749033266035 y[1] (numeric) = -1.346749033266003 absolute error = 3.219646771412954e-14 relative error = 2.390680588502007e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.37 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] = 2.879999999999992 y[1] (analytic) = -1.323891880457475 y[1] (numeric) = -1.323891880457443 absolute error = 3.241851231905457e-14 relative error = 2.448728087058911e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.38 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] = 2.889999999999992 y[1] (analytic) = -1.301086853470223 y[1] (numeric) = -1.30108685347019 absolute error = 3.241851231905457e-14 relative error = 2.491648596140128e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.39 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] = 2.899999999999991 y[1] (analytic) = -1.278333715098868 y[1] (numeric) = -1.278333715098835 absolute error = 3.26405569239796e-14 relative error = 2.553367445327463e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.4 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] = 2.909999999999991 y[1] (analytic) = -1.255632229753476 y[1] (numeric) = -1.255632229753443 absolute error = 3.308464613382966e-14 relative error = 2.634899403651443e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.41 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] = 2.919999999999991 y[1] (analytic) = -1.232982163444957 y[1] (numeric) = -1.232982163444922 absolute error = 3.574918139293004e-14 relative error = 2.899407830284153e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.42 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] = 2.929999999999991 y[1] (analytic) = -1.210383283770582 y[1] (numeric) = -1.210383283770546 absolute error = 3.597122599785507e-14 relative error = 2.971887209628145e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.43 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] = 2.939999999999991 y[1] (analytic) = -1.187835359899691 y[1] (numeric) = -1.187835359899655 absolute error = 3.641531520770513e-14 relative error = 3.065687084006347e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.44 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] = 2.94999999999999 y[1] (analytic) = -1.165338162559536 y[1] (numeric) = -1.1653381625595 absolute error = 3.641531520770513e-14 relative error = 3.124871078427821e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.45 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] = 2.95999999999999 y[1] (analytic) = -1.142891464021298 y[1] (numeric) = -1.142891464021261 absolute error = 3.663735981263017e-14 relative error = 3.205672713988127e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.46 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] = 2.96999999999999 y[1] (analytic) = -1.120495038086252 y[1] (numeric) = -1.120495038086213 absolute error = 3.930189507173054e-14 relative error = 3.507547444284639e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.47 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] = 2.97999999999999 y[1] (analytic) = -1.098148660072089 y[1] (numeric) = -1.09814866007205 absolute error = 3.952393967665557e-14 relative error = 3.599142913315669e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.48 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] = 2.98999999999999 y[1] (analytic) = -1.075852106799398 y[1] (numeric) = -1.075852106799358 absolute error = 3.97459842815806e-14 relative error = 3.694372491384784e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.49 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] = 2.999999999999989 y[1] (analytic) = -1.053605156578286 y[1] (numeric) = -1.053605156578246 absolute error = 3.996802888650564e-14 relative error = 3.793454183188205e-12 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.5 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] = 3.009999999999989 y[1] (analytic) = -1.031407589195157 y[1] (numeric) = -1.031407589195117 absolute error = 4.019007349143067e-14 relative error = 3.896623789901757e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.51 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] = 3.019999999999989 y[1] (analytic) = -1.009259185899629 y[1] (numeric) = -1.009259185899588 absolute error = 4.04121180963557e-14 relative error = 4.004136762979604e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.52 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] = 3.029999999999989 y[1] (analytic) = -0.9871597293916026 y[1] (numeric) = -0.9871597293915597 absolute error = 4.285460875053104e-14 relative error = 4.341203097592201e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.53 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] = 3.039999999999988 y[1] (analytic) = -0.965109003808463 y[1] (numeric) = -0.9651090038084198 absolute error = 4.318767565791859e-14 relative error = 4.474901331092511e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.54 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] = 3.049999999999988 y[1] (analytic) = -0.9431067947124385 y[1] (numeric) = -0.9431067947123952 absolute error = 4.329869796038111e-14 relative error = 4.591070513237396e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.55 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] = 3.059999999999988 y[1] (analytic) = -0.9211528890780818 y[1] (numeric) = -0.9211528890780384 absolute error = 4.340972026284362e-14 relative error = 4.712542377877076e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.56 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] = 3.069999999999988 y[1] (analytic) = -0.8992470752798956 y[1] (numeric) = -0.8992470752798519 absolute error = 4.363176486776865e-14 relative error = 4.852033002630343e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.57 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] = 3.079999999999988 y[1] (analytic) = -0.8773891430800953 y[1] (numeric) = -0.8773891430800491 absolute error = 4.618527782440651e-14 relative error = 5.263944532328267e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.58 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] = 3.089999999999987 y[1] (analytic) = -0.8555788836164934 y[1] (numeric) = -0.855578883616447 absolute error = 4.640732242933154e-14 relative error = 5.42408459558631e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.59 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] = 3.099999999999987 y[1] (analytic) = -0.8338160893905379 y[1] (numeric) = -0.8338160893904915 absolute error = 4.640732242933154e-14 relative error = 5.565654467432033e-12 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 4.6 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 Finished! diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; Iterations = 61 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 103.3 %