##############ECHO OF PROBLEM################# ##############temp/nonlinear2postode.ode################# diff ( y , x , 1 ) = y * y ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb x_start=0.0 x_end=0.2 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_max_h=0.5 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=0.5 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(2.0/(1.0 - 2.0*x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 0.2 estimated_steps 200000.00000000003 step_error 4.999999999999999e-16 est_needed_step_err 4.999999999999999e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3107213107213108e-91 estimated_step_error 1.3107213107213108e-91 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.589951771903542e-87 estimated_step_error 8.589951771903542e-87 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.629522052301328e-82 estimated_step_error 5.629522052301328e-82 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.6893783297685475e-77 estimated_step_error 3.6893783297685475e-77 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.417890325474466e-72 estimated_step_error 2.417890325474466e-72 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5846139579319407e-67 estimated_step_error 1.5846139579319407e-67 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0385258373605564e-62 estimated_step_error 1.0385258373605564e-62 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.806518572796085e-58 estimated_step_error 6.806518572796085e-58 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.461291130235445e-53 estimated_step_error 4.461291130235445e-53 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.9245006189785214e-48 estimated_step_error 2.9245006189785214e-48 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.917583031104105e-43 estimated_step_error 1.917583031104105e-43 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2579967243467127e-38 estimated_step_error 1.2579967243467127e-38 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.261361320257963e-34 estimated_step_error 8.261361320257963e-34 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.436525324605938e-29 estimated_step_error 5.436525324605938e-29 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.592554284321596e-24 estimated_step_error 3.592554284321596e-24 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.3942953859699935e-19 estimated_step_error 2.3942953859699935e-19 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6241204318647624e-14 estimated_step_error 1.6241204318647624e-14 best_h 0.032768 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (analytic) 2.0 y[1] (numeric) 2.0 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4999999999999964 Order of pole (three term test) 0.9999999999998763 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.01 y[1] (analytic) 2.0408163265306123 y[1] (numeric) 2.0408163265306123 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.49 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.49 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.49000000000000066 Order of pole (three term test) 1.0000000000000597 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.02 y[1] (analytic) 2.0833333333333335 y[1] (numeric) 2.0833333333333335 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.48 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4799999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4800000000000044 Order of pole (three term test) 1.000000000000155 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.03 y[1] (analytic) 2.127659574468085 y[1] (numeric) 2.127659574468085 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.47 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.47000000000000003 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4700000000000006 Order of pole (three term test) 1.0000000000000226 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04 y[1] (analytic) 2.1739130434782608 y[1] (numeric) 2.1739130434782608 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.46 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4599999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4599999999999997 Order of pole (three term test) 0.9999999999999903 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05 y[1] (analytic) 2.2222222222222223 y[1] (numeric) 2.2222222222222223 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.45 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.45000000000000007 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.450000000000002 Order of pole (three term test) 1.0000000000000544 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.060000000000000005 y[1] (analytic) 2.272727272727273 y[1] (numeric) 2.272727272727273 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.44 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.43999999999999995 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.43999999999999906 Order of pole (three term test) 0.9999999999999579 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07 y[1] (analytic) 2.3255813953488373 y[1] (numeric) 2.3255813953488373 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.43 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4300000000000001 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.42999999999999833 Order of pole (three term test) 0.9999999999999564 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08 y[1] (analytic) 2.380952380952381 y[1] (numeric) 2.380952380952381 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.42 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.42000000000000015 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4199999999999972 Order of pole (three term test) 0.9999999999999075 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09 y[1] (analytic) 2.4390243902439024 y[1] (numeric) 2.4390243902439024 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.41000000000000003 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.41 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.40999999999999914 Order of pole (three term test) 1.0000000000000093 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09999999999999999 y[1] (analytic) 2.5 y[1] (numeric) 2.5 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.4 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.4 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.40000000000000213 Order of pole (three term test) 1.0000000000001157 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10999999999999999 y[1] (analytic) 2.564102564102564 y[1] (numeric) 2.564102564102564 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.39 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.38999999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.39000000000000223 Order of pole (three term test) 1.0000000000000315 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11999999999999998 y[1] (analytic) 2.6315789473684212 y[1] (numeric) 2.631578947368421 absolute error 4.440892098500626e-16 relative error 1.687538997430238e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.38 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.37999999999999995 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.380000000000004 Order of pole (three term test) 1.0000000000001477 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12999999999999998 y[1] (analytic) 2.7027027027027026 y[1] (numeric) 2.7027027027027026 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.37 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.36999999999999994 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.37000000000000166 Order of pole (three term test) 1.0000000000000313 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13999999999999999 y[1] (analytic) 2.7777777777777777 y[1] (numeric) 2.7777777777777777 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.36 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3600000000000001 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.3600000000000001 Order of pole (three term test) 1.0000000000000173 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15 y[1] (analytic) 2.857142857142857 y[1] (numeric) 2.857142857142857 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.35 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.35 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.35000000000000037 Order of pole (three term test) 0.9999999999999961 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16 y[1] (analytic) 2.9411764705882355 y[1] (numeric) 2.9411764705882355 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.33999999999999997 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3399999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.34 Order of pole (three term test) 1.0000000000000089 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17 y[1] (analytic) 3.0303030303030307 y[1] (numeric) 3.0303030303030307 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.32999999999999996 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.32999999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.32999999999999924 Order of pole (three term test) 0.9999999999999929 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000002 y[1] (analytic) 3.1250000000000004 y[1] (numeric) 3.1250000000000004 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.31999999999999995 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.3199999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.32000000000000184 Order of pole (three term test) 1.000000000000093 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000003 y[1] (analytic) 3.225806451612904 y[1] (numeric) 3.225806451612904 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.30999999999999994 Order of pole (given) 0.0 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 0.30999999999999994 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.31000000000000044 Order of pole (three term test) 1.0000000000000093 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y ; Iterations 20 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 10 Minutes 0.0 Seconds Percent Done 105.00000000000001%