##############ECHO OF PROBLEM################# ##############temp/sing6_backpostode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=30; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=3.0 x_end=2.0 # ELIMINATED in preodein.rb $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 $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=6.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=3.0 # 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 - 6.0 ) / ( x - 6.0 )) 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 -1.0 estimated_steps 1000000.0 step_error 5.0e-21 est_needed_step_err 5.0e-21 opt_iter 1 min_size 0.1111111111111111 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 -1.0 estimated_steps 1000000.0 step_error 5.0e-21 est_needed_step_err 5.0e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.839701975293304e-105 estimated_step_error 4.839701975293304e-105 Double H and LOOP opt_iter 2 min_size 0.1111111111111111 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 -1.0 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 3.171746588999422e-100 estimated_step_error 3.171746588999422e-100 Double H and LOOP opt_iter 3 min_size 0.1111111111111111 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 -1.0 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 2.0786351924460232e-95 estimated_step_error 2.0786351924460232e-95 Double H and LOOP opt_iter 4 min_size 0.1111111111111111 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 -1.0 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 1.3622535049746704e-90 estimated_step_error 1.3622535049746704e-90 Double H and LOOP opt_iter 5 min_size 0.1111111111111111 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 -1.0 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 8.927653366886491e-86 estimated_step_error 8.927653366886491e-86 Double H and LOOP opt_iter 6 min_size 0.1111111111111111 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 -1.0 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 5.850812226168499e-81 estimated_step_error 5.850812226168499e-81 Double H and LOOP opt_iter 7 min_size 0.1111111111111111 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 -1.0 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 3.834369053610431e-76 estimated_step_error 3.834369053610431e-76 Double H and LOOP opt_iter 8 min_size 0.1111111111111111 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 -1.0 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 2.51286687601747e-71 estimated_step_error 2.51286687601747e-71 Double H and LOOP opt_iter 9 min_size 0.1111111111111111 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 -1.0 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 1.6467993713894443e-66 estimated_step_error 1.6467993713894443e-66 Double H and LOOP opt_iter 10 min_size 0.1111111111111111 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 -1.0 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 1.0792031003813601e-61 estimated_step_error 1.0792031003813601e-61 Double H and LOOP opt_iter 11 min_size 0.1111111111111111 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 -1.0 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 7.072097498250659e-57 estimated_step_error 7.072097498250659e-57 Double H and LOOP opt_iter 12 min_size 0.1111111111111111 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 -1.0 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 4.634025585524804e-52 estimated_step_error 4.634025585524804e-52 Double H and LOOP opt_iter 13 min_size 0.1111111111111111 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 -1.0 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 3.035980000758586e-47 estimated_step_error 3.035980000758586e-47 Double H and LOOP opt_iter 14 min_size 0.1111111111111111 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 -1.0 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 1.9883831264858017e-42 estimated_step_error 1.9883831264858017e-42 Double H and LOOP opt_iter 15 min_size 0.1111111111111111 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 -1.0 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 1.3014365627772145e-37 estimated_step_error 1.3014365627772145e-37 Double H and LOOP opt_iter 16 min_size 0.1111111111111111 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 -1.0 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 8.507287217999273e-33 estimated_step_error 8.507287217999273e-33 Double H and LOOP opt_iter 17 min_size 0.1111111111111111 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 -1.0 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 5.5469711287651505e-28 estimated_step_error 5.5469711287651505e-28 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] 2.9 y[1] (closed_form) 0.1040582726326743 y[1] (numeric) 0.10405827234586033 absolute error 2.8681396146978955e-10 relative error 2.7562821697246775e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h -0.1 Radius of convergence (given) for eq 1 3.1 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.100000000000007 Order of pole (three term test) 2.4911144204099666e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8 y[1] (closed_form) 0.09765625 y[1] (numeric) 0.0976562494921224 absolute error 5.078776010858377e-10 relative error 5.200666635118978e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h -0.1 Radius of convergence (given) for eq 1 3.2 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.2000000000000006 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6999999999999997 y[1] (closed_form) 0.09182736455463726 y[1] (numeric) 0.09182736387496891 absolute error 6.796683493792699e-10 relative error 7.401588324740251e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h -0.1 Radius of convergence (given) for eq 1 3.3000000000000003 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.300000000000023 Order of pole (three term test) 8.127015001308478e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5999999999999996 y[1] (closed_form) 0.08650519031141866 y[1] (numeric) 0.08650518949721703 absolute error 8.142016366674554e-10 relative error 9.412170919875786e-07% Desired digits 16 Estimated correct digits 13 Correct digits 9 h -0.1 Radius of convergence (given) for eq 1 3.4000000000000004 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.399999999999997 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4999999999999996 y[1] (closed_form) 0.08163265306122447 y[1] (numeric) 0.08163265214090006 absolute error 9.203244138999978e-10 relative error 1.1273974070274975e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h -0.1 Radius of convergence (given) for eq 1 3.5000000000000004 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.500000000000015 Order of pole (three term test) 5.93559429285342e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3999999999999995 y[1] (closed_form) 0.07716049382716048 y[1] (numeric) 0.07716049282255018 absolute error 1.0046102977279148e-09 relative error 1.3019749458553778e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h -0.1 Radius of convergence (given) for eq 1 3.6000000000000005 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.600000000000008 Order of pole (three term test) 3.454919317361569e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2999999999999994 y[1] (closed_form) 0.07304601899196492 y[1] (numeric) 0.07304601791997908 absolute error 1.0719858334340415e-09 relative error 1.4675486059712033e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h -0.1 Radius of convergence (given) for eq 1 3.7000000000000006 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.7000000000000184 Order of pole (three term test) 7.859856349762688e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1999999999999993 y[1] (closed_form) 0.06925207756232683 y[1] (numeric) 0.06925207643615361 absolute error 1.1261732241196754e-09 relative error 1.626194135628812e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h -0.1 Radius of convergence (given) for eq 1 3.8000000000000007 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.800000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.099999999999999 y[1] (closed_form) 0.06574621959237341 y[1] (numeric) 0.06574621842236704 absolute error 1.1700063695663232e-09 relative error 1.7795796881103784e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h -0.1 Radius of convergence (given) for eq 1 3.900000000000001 Order of pole (given) 3.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 3.90000000000002 Order of pole (three term test) 4.766626362037105e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; 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%