##############ECHO OF PROBLEM################# ##############temp/sing5_backpostode.ode################# diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-0.7 x_end=-1.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # 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]=0.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=4.0 # 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/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 16 estimated_h -1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range -0.30000000000000004 estimated_steps 300000.00000000006 step_error 9.128709291752767e-21 est_needed_step_err 9.128709291752767e-21 opt_iter 1 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -1.0e-06 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 300000.00000000006 step_error 2.6614312803943934e-20 est_needed_step_err 2.6614312803943934e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.75713302168016e-93 estimated_step_error 5.75713302168016e-93 Double H and LOOP opt_iter 2 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -2.0e-06 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 150000.00000000003 step_error 3.763832212057742e-20 est_needed_step_err 3.763832212057742e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.772992160624715e-88 estimated_step_error 3.772992160624715e-88 Double H and LOOP opt_iter 3 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -4.0e-06 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 75000.00000000001 step_error 5.322862560788787e-20 est_needed_step_err 5.322862560788787e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.472664817800178e-83 estimated_step_error 2.472664817800178e-83 Double H and LOOP opt_iter 4 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -8.0e-06 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 37500.00000000001 step_error 7.527664424115484e-20 est_needed_step_err 7.527664424115484e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6204812574087059e-78 estimated_step_error 1.6204812574087059e-78 Double H and LOOP opt_iter 5 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -1.6e-05 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 18750.000000000004 step_error 1.0645725121577574e-19 est_needed_step_err 1.0645725121577574e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0619928853280323e-73 estimated_step_error 1.0619928853280323e-73 Double H and LOOP opt_iter 6 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -3.2e-05 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 9375.000000000002 step_error 1.505532884823097e-19 est_needed_step_err 1.505532884823097e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.9598017123667e-69 estimated_step_error 6.9598017123667e-69 Double H and LOOP opt_iter 7 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -6.4e-05 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 4687.500000000001 step_error 2.1291450243155147e-19 est_needed_step_err 2.1291450243155147e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.561077531689908e-64 estimated_step_error 4.561077531689908e-64 Double H and LOOP opt_iter 8 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.000128 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 2343.7500000000005 step_error 3.011065769646194e-19 est_needed_step_err 3.011065769646194e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.989019173580979e-59 estimated_step_error 2.989019173580979e-59 Double H and LOOP opt_iter 9 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.000256 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 1171.8750000000002 step_error 4.2582900486310294e-19 est_needed_step_err 4.2582900486310294e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.958715071996529e-54 estimated_step_error 1.958715071996529e-54 Double H and LOOP opt_iter 10 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.000512 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 585.9375000000001 step_error 6.022131539292388e-19 est_needed_step_err 6.022131539292388e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2834426664253182e-49 estimated_step_error 1.2834426664253182e-49 Double H and LOOP opt_iter 11 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.001024 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 292.96875000000006 step_error 8.516580097262059e-19 est_needed_step_err 8.516580097262059e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.408276721894535e-45 estimated_step_error 8.408276721894535e-45 Double H and LOOP opt_iter 12 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.002048 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 146.48437500000003 step_error 1.2044263078584775e-18 est_needed_step_err 1.2044263078584775e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.50666006406965e-40 estimated_step_error 5.50666006406965e-40 Double H and LOOP opt_iter 13 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.004096 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 73.24218750000001 step_error 1.7033160194524118e-18 est_needed_step_err 1.7033160194524118e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.603889772678617e-35 estimated_step_error 3.603889772678617e-35 Double H and LOOP opt_iter 14 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.008192 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 36.62109375000001 step_error 2.408852615716955e-18 est_needed_step_err 2.408852615716955e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.3553773951085728e-30 estimated_step_error 2.3553773951085728e-30 Double H and LOOP opt_iter 15 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.016384 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 18.310546875000004 step_error 3.4066320389048235e-18 est_needed_step_err 3.4066320389048235e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5352121296515697e-25 estimated_step_error 1.5352121296515697e-25 Double H and LOOP opt_iter 16 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.032768 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 9.155273437500002 step_error 4.81770523143391e-18 est_needed_step_err 4.81770523143391e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.95274629323742e-21 estimated_step_error 9.95274629323742e-21 Double H and LOOP opt_iter 17 min_size 2.915451895043732 $glob_desired_digits_correct 16 estimated_h -0.065536 estimated_answer 2.915451895043732 desired_abs_gbl_error 2.915451895043732e-16 range -0.30000000000000004 estimated_steps 4.577636718750001 step_error 6.813264077809647e-18 est_needed_step_err 6.813264077809647e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.385015069955109e-16 estimated_step_error 6.385015069955109e-16 Found H for OPTIMAL START of Soultion TOP MAIN SOLVE Loop x[1] -0.732768 y[1] (closed_form) -2.5415608599682322 y[1] (numeric) -2.541560565999402 absolute error 2.939688301673016e-07 relative error 1.1566468259625936e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 0.732768 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7327680000000004 Order of pole (three term test) 4.69262882318016e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.831072 y[1] (closed_form) -1.7421439951622 y[1] (numeric) -1.7421432821933824 absolute error 7.129688175400162e-07 relative error 4.0924792641703314e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 0.831072 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8310720000000043 Order of pole (three term test) 8.237116148217375e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9293760000000001 y[1] (closed_form) -1.2457349254569736 y[1] (numeric) -1.2457340715155856 absolute error 8.539413880459534e-07 relative error 6.854920501909358e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 0.9293760000000001 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9293760000000026 Order of pole (three term test) 4.605586031463535e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations 10 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%