##############ECHO OF PROBLEM################# ##############temp/sing1_backpostode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb 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_max_h=0.1 # 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=2 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.001 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=1.0 # ELIMINATED in preodein.rb $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 def exact_soln_y (x) return(1.0 / (x * x + 0.000001)) 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 16 estimated_h -1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 500000.0 step_error 7.071067811865475e-21 est_needed_step_err 7.071067811865475e-21 opt_iter 1 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 500000.0 step_error 7.071067811865475e-21 est_needed_step_err 7.071067811865475e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1502575775107897e-98 estimated_step_error 1.1502575775107897e-98 Double H and LOOP opt_iter 2 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -2.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 250000.0 step_error 1.0e-20 est_needed_step_err 1.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.538325399397697e-94 estimated_step_error 7.538325399397697e-94 Double H and LOOP opt_iter 3 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -4.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 125000.0 step_error 1.414213562373095e-20 est_needed_step_err 1.414213562373095e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.940313446481449e-89 estimated_step_error 4.940313446481449e-89 Double H and LOOP opt_iter 4 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -8.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 62500.0 step_error 2.0e-20 est_needed_step_err 2.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.2376792494640484e-84 estimated_step_error 3.2376792494640484e-84 Double H and LOOP opt_iter 5 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -1.6e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 31250.0 step_error 2.82842712474619e-20 est_needed_step_err 2.82842712474619e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.121839481886198e-79 estimated_step_error 2.121839481886198e-79 Double H and LOOP opt_iter 6 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -3.2e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 15625.0 step_error 4.0e-20 est_needed_step_err 4.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3905608703359428e-74 estimated_step_error 1.3905608703359428e-74 Double H and LOOP opt_iter 7 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -6.4e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 7812.5 step_error 5.65685424949238e-20 est_needed_step_err 5.65685424949238e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.113076797113529e-70 estimated_step_error 9.113076797113529e-70 Double H and LOOP opt_iter 8 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.000128 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 3906.25 step_error 8.0e-20 est_needed_step_err 8.0e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.972211111445129e-65 estimated_step_error 5.972211111445129e-65 Double H and LOOP opt_iter 9 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.000256 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 1953.125 step_error 1.131370849898476e-19 est_needed_step_err 1.131370849898476e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.913771472025888e-60 estimated_step_error 3.913771472025888e-60 Double H and LOOP opt_iter 10 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.000512 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 976.5625 step_error 1.6e-19 est_needed_step_err 1.6e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.5646975653323848e-55 estimated_step_error 2.5646975653323848e-55 Double H and LOOP opt_iter 11 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.001024 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 488.28125 step_error 2.262741699796952e-19 est_needed_step_err 2.262741699796952e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6804965760123694e-50 estimated_step_error 1.6804965760123694e-50 Double H and LOOP opt_iter 12 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.002048 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 244.140625 step_error 3.2e-19 est_needed_step_err 3.2e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1009324896407096e-45 estimated_step_error 1.1009324896407096e-45 Double H and LOOP opt_iter 13 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.004096 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 122.0703125 step_error 4.525483399593904e-19 est_needed_step_err 4.525483399593904e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.209863449232822e-41 estimated_step_error 7.209863449232822e-41 Double H and LOOP opt_iter 14 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.008192 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 61.03515625 step_error 6.4e-19 est_needed_step_err 6.4e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.718244967515527e-36 estimated_step_error 4.718244967515527e-36 Double H and LOOP opt_iter 15 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.016384 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 30.517578125 step_error 9.050966799187808e-19 est_needed_step_err 9.050966799187808e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.083259896597151e-31 estimated_step_error 3.083259896597151e-31 Double H and LOOP opt_iter 16 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.032768 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 15.2587890625 step_error 1.28e-18 est_needed_step_err 1.28e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0090936281784452e-26 estimated_step_error 2.0090936281784452e-26 Double H and LOOP opt_iter 17 min_size 0.444444246913668 min_size 1.0 $glob_desired_digits_correct 16 estimated_h -0.065536 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.5 estimated_steps 7.62939453125 step_error 1.8101933598375616e-18 est_needed_step_err 1.8101933598375616e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3017943905559768e-21 estimated_step_error 1.3017943905559768e-21 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] -1.6 y[1] (closed_form) 0.3906248474121689 y[1] (numeric) 0.39062484741216896 absolute error 5.551115123125783e-17 relative error 1.421086026631713e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.6000003124999698 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6000062500747076 Order of pole (three term test) 2.0000273442135525 Radius of convergence (six term test) for eq 1 1.6000002092275922 Order of pole (six term test) 1.0000000000071037 TOP MAIN SOLVE Loop x[1] -1.7000000000000002 y[1] (closed_form) 0.3460206415153489 y[1] (numeric) 0.34602064151534895 absolute error 5.551115123125783e-17 relative error 1.6042728256948637e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.7000002941176218 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7000058824152304 Order of pole (three term test) 2.000024221817102 Radius of convergence (six term test) for eq 1 1.70000011878015 Order of pole (six term test) 1.000000000009475 TOP MAIN SOLVE Loop x[1] -1.8000000000000003 y[1] (closed_form) 0.30864188004880233 y[1] (numeric) 0.30864188004880244 absolute error 1.1102230246251565e-16 relative error 3.5971237100085334e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.8000002777777566 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8000055556080332 Order of pole (three term test) 2.000021605227705 Radius of convergence (six term test) for eq 1 1.799999856994214 Order of pole (six term test) 1.0000000000204272 TOP MAIN SOLVE Loop x[1] -1.9000000000000004 y[1] (closed_form) 0.2770082335157247 y[1] (numeric) 0.2770082335157248 absolute error 1.1102230246251565e-16 relative error 4.0079062291198414e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h -0.1 Radius of convergence (given) for eq 1 1.900000263157877 Order of pole (given) 1.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.9000052632025024 Order of pole (three term test) 2.0000193908147805 Radius of convergence (six term test) for eq 1 1.9000001603061294 Order of pole (six term test) 1.000000000004741 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations 5 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Expected Time Remaining 0.0 Seconds Optimized Time Remaining 0.0 Seconds Expected Total Time 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 0.0%