##############ECHO OF PROBLEM################# ##############temp/sing5postode.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=-1.0 x_end=-0.7 $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 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.562503088236751e-96 estimated_step_error 6.562503088236751e-96 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 150000.00000000003 step_error 1.2909944487358053e-20 est_needed_step_err 1.2909944487358053e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.3008040478155865e-91 estimated_step_error 4.3008040478155865e-91 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 75000.00000000001 step_error 1.8257418583505535e-20 est_needed_step_err 1.8257418583505535e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.818577593557857e-86 estimated_step_error 2.818577593557857e-86 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 37500.00000000001 step_error 2.5819888974716106e-20 est_needed_step_err 2.5819888974716106e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8471864887776104e-81 estimated_step_error 1.8471864887776104e-81 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 18750.000000000004 step_error 3.651483716701107e-20 est_needed_step_err 3.651483716701107e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.210576694767835e-76 estimated_step_error 1.210576694767835e-76 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 9375.000000000002 step_error 5.163977794943221e-20 est_needed_step_err 5.163977794943221e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.93369516334265e-72 estimated_step_error 7.93369516334265e-72 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 4687.500000000001 step_error 7.302967433402214e-20 est_needed_step_err 7.302967433402214e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.199504761864271e-67 estimated_step_error 5.199504761864271e-67 Double H and LOOP opt_iter 8 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 2343.7500000000005 step_error 1.0327955589886442e-19 est_needed_step_err 1.0327955589886442e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.407650074260886e-62 estimated_step_error 3.407650074260886e-62 Double H and LOOP opt_iter 9 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 1171.8750000000002 step_error 1.4605934866804428e-19 est_needed_step_err 1.4605934866804428e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2333720886804876e-57 estimated_step_error 2.2333720886804876e-57 Double H and LOOP opt_iter 10 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 585.9375000000001 step_error 2.0655911179772885e-19 est_needed_step_err 2.0655911179772885e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4638391030643554e-52 estimated_step_error 1.4638391030643554e-52 Double H and LOOP opt_iter 11 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 292.96875000000006 step_error 2.9211869733608856e-19 est_needed_step_err 2.9211869733608856e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.595728514958766e-48 estimated_step_error 9.595728514958766e-48 Double H and LOOP opt_iter 12 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 146.48437500000003 step_error 4.131182235954577e-19 est_needed_step_err 4.131182235954577e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.291689970870765e-43 estimated_step_error 6.291689970870765e-43 Double H and LOOP opt_iter 13 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 73.24218750000001 step_error 5.842373946721771e-19 est_needed_step_err 5.842373946721771e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.1273035661418647e-38 estimated_step_error 4.1273035661418647e-38 Double H and LOOP opt_iter 14 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 36.62109375000001 step_error 8.262364471909154e-19 est_needed_step_err 8.262364471909154e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.7101036631217316e-33 estimated_step_error 2.7101036631217316e-33 Double H and LOOP opt_iter 15 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000001 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 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 0.30000000000000004 estimated_steps 18.310546875000004 step_error 1.1684747893443542e-18 est_needed_step_err 1.1684747893443542e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.782993957434995e-28 estimated_step_error 1.782993957434995e-28 Double H and LOOP opt_iter 16 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9155273437500011 Order of pole (three term test) 2.999427820665636e-14 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (closed_form) -1.0 y[1] (numeric) -1.0 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.030000000000000006 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.000000000000004 Order of pole (three term test) 3.719581805093087e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.97 y[1] (closed_form) -1.0956826815299676 y[1] (numeric) -1.0956826733943974 absolute error 8.13557021750455e-09 relative error 7.42511527712053e-07% Desired digits 16 Estimated correct digits 14 Correct digits 9 h 0.030000000000000006 Radius of convergence (given) for eq 1 0.97 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9700000000000053 Order of pole (three term test) 8.420557805106688e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.94 y[1] (closed_form) -1.2039721449004557 y[1] (numeric) -1.2039721260429164 absolute error 1.8857539307859383e-08 relative error 1.5662770428479076e-06% Desired digits 16 Estimated correct digits 14 Correct digits 8 h 0.030000000000000006 Radius of convergence (given) for eq 1 0.94 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9400000000000059 Order of pole (three term test) 4.108425506552547e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9099999999999999 y[1] (closed_form) -1.3270149727099374 y[1] (numeric) -1.3270149395977766 absolute error 3.311216079104895e-08 relative error 2.4952364119471543e-06% Desired digits 16 Estimated correct digits 14 Correct digits 8 h 0.030000000000000006 Radius of convergence (given) for eq 1 0.9099999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9100000000000027 Order of pole (three term test) 5.820611958358121e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8799999999999999 y[1] (closed_form) -1.4674117205108945 y[1] (numeric) -1.4674116682702962 absolute error 5.2240598291675155e-08 relative error 3.560050499902444e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.030000000000000006 Radius of convergence (given) for eq 1 0.8799999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8800000000000034 Order of pole (three term test) 7.964336353751278e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8499999999999999 y[1] (closed_form) -1.6283329940972937 y[1] (numeric) -1.6283329159316637 absolute error 7.816562996865173e-08 relative error 4.800346750449822e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.030000000000000006 Radius of convergence (given) for eq 1 0.8499999999999999 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8500000000000013 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8199999999999998 y[1] (closed_form) -1.813670724452635 y[1] (numeric) -1.8136706107748466 absolute error 1.1367778851578692e-07 relative error 6.267829489837237e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.030000000000000006 Radius of convergence (given) for eq 1 0.8199999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8200000000000014 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7899999999999998 y[1] (closed_form) -2.0282371171448927 y[1] (numeric) -2.0282369542645466 absolute error 1.628803460995698e-07 relative error 8.030636296058573e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h 0.030000000000000006 Radius of convergence (given) for eq 1 0.7899999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7899999999999999 Order of pole (three term test) 4.035440871007176e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7599999999999998 y[1] (closed_form) -2.2780288671818067 y[1] (numeric) -2.278028635289597 absolute error 2.3189220987873682e-07 relative error 1.0179511472372829e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.030000000000000006 Radius of convergence (given) for eq 1 0.7599999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.760000000000003 Order of pole (three term test) 4.676479245320192e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7299999999999998 y[1] (closed_form) -2.570581748355473 y[1] (numeric) -2.570581418378468 absolute error 3.299770048315054e-07 relative error 1.283666644885376e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.030000000000000006 Radius of convergence (given) for eq 1 0.7299999999999998 Order of pole (given) 4.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7300000000000008 Order of pole (three term test) 5.1555567702701605e-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 Time to Timeout 3 Minutes 0.0 Seconds Percent Done 110.00000000000009%