##############ECHO OF PROBLEM################# ##############temp/sing3_backpostode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / 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=-2.0 $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]=2.0 # 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) 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 -1.3 estimated_steps 1300000.0 step_error 4.385290096535146e-21 est_needed_step_err 4.385290096535146e-21 opt_iter 1 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -1.0e-06 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 1300000.0 step_error 8.94957162558193e-21 est_needed_step_err 8.94957162558193e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1514266043360324e-93 estimated_step_error 1.1514266043360324e-93 Double H and LOOP opt_iter 2 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -2.0e-06 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 650000.0 step_error 1.2656605570327395e-20 est_needed_step_err 1.2656605570327395e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.545984321249431e-89 estimated_step_error 7.545984321249431e-89 Double H and LOOP opt_iter 3 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -4.0e-06 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 325000.0 step_error 1.789914325116386e-20 est_needed_step_err 1.789914325116386e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.945329635600357e-84 estimated_step_error 4.945329635600357e-84 Double H and LOOP opt_iter 4 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -8.0e-06 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 162500.0 step_error 2.531321114065479e-20 est_needed_step_err 2.531321114065479e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.2409625148174126e-79 estimated_step_error 3.2409625148174126e-79 Double H and LOOP opt_iter 5 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -1.6e-05 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 81250.0 step_error 3.579828650232772e-20 est_needed_step_err 3.579828650232772e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.1239857706560644e-74 estimated_step_error 2.1239857706560644e-74 Double H and LOOP opt_iter 6 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -3.2e-05 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 40625.0 step_error 5.062642228130958e-20 est_needed_step_err 5.062642228130958e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3919603424733406e-69 estimated_step_error 1.3919603424733406e-69 Double H and LOOP opt_iter 7 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -6.4e-05 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 20312.5 step_error 7.159657300465544e-20 est_needed_step_err 7.159657300465544e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.122155063379819e-65 estimated_step_error 9.122155063379819e-65 Double H and LOOP opt_iter 8 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.000128 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 10156.25 step_error 1.0125284456261916e-19 est_needed_step_err 1.0125284456261916e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.97803834716196e-60 estimated_step_error 5.97803834716196e-60 Double H and LOOP opt_iter 9 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.000256 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 5078.125 step_error 1.4319314600931088e-19 est_needed_step_err 1.4319314600931088e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.917430143993059e-55 estimated_step_error 3.917430143993059e-55 Double H and LOOP opt_iter 10 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.000512 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 2539.0625 step_error 2.0250568912523833e-19 est_needed_step_err 2.0250568912523833e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.566885332850637e-50 estimated_step_error 2.566885332850637e-50 Double H and LOOP opt_iter 11 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.001024 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 1269.53125 step_error 2.8638629201862175e-19 est_needed_step_err 2.8638629201862175e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6816553443789073e-45 estimated_step_error 1.6816553443789073e-45 Double H and LOOP opt_iter 12 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.002048 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 634.765625 step_error 4.0501137825047666e-19 est_needed_step_err 4.0501137825047666e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1013320128139303e-40 estimated_step_error 1.1013320128139303e-40 Double H and LOOP opt_iter 13 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.004096 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 317.3828125 step_error 5.727725840372435e-19 est_needed_step_err 5.727725840372435e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.207779545357236e-36 estimated_step_error 7.207779545357236e-36 Double H and LOOP opt_iter 14 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.008192 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 158.69140625 step_error 8.100227565009533e-19 est_needed_step_err 8.100227565009533e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.710754790217147e-31 estimated_step_error 4.710754790217147e-31 Double H and LOOP opt_iter 15 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.016384 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 79.345703125 step_error 1.145545168074487e-18 est_needed_step_err 1.145545168074487e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.0704242593031406e-26 estimated_step_error 3.0704242593031406e-26 Double H and LOOP opt_iter 16 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.032768 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 39.6728515625 step_error 1.6200455130019066e-18 est_needed_step_err 1.6200455130019066e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9905492586474845e-21 estimated_step_error 1.9905492586474845e-21 Double H and LOOP opt_iter 17 min_size 2.0408163265306123 $glob_desired_digits_correct 16 estimated_h -0.065536 estimated_answer 2.0408163265306123 desired_abs_gbl_error 2.0408163265306123e-16 range -1.3 estimated_steps 19.83642578125 step_error 2.291090336148974e-18 est_needed_step_err 2.291090336148974e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2770030139910218e-16 estimated_step_error 1.2770030139910218e-16 Found H for OPTIMAL START of Soultion TOP MAIN SOLVE Loop x[1] -0.732768 y[1] (closed_form) 1.8623744682372017 y[1] (numeric) 1.8623744287895527 absolute error 3.9447648925161616e-08 relative error 2.118137334781018e-06% Desired digits 16 Estimated correct digits 14 Correct digits 8 h -0.032768 Radius of convergence (given) for eq 1 0.732768 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7327679999999994 Order of pole (three term test) 3.3455638543049304e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.86384 y[1] (closed_form) 1.3400881897243082 y[1] (numeric) 1.3400880793461443 absolute error 1.1037816394221522e-07 relative error 8.236634334112215e-06% Desired digits 16 Estimated correct digits 13 Correct digits 8 h -0.032768 Radius of convergence (given) for eq 1 0.86384 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8638400000000042 Order of pole (three term test) 7.282722979340752e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9949120000000001 y[1] (closed_form) 1.0102541934708233 y[1] (numeric) 1.0102540627571404 absolute error 1.3071368298867014e-07 relative error 1.2938692443293998e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 0.9949120000000001 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9949120000000072 Order of pole (three term test) 7.882329496205643e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1259839999999999 y[1] (closed_form) 0.788743078809519 y[1] (numeric) 0.7887429411783439 absolute error 1.3763117512333167e-07 relative error 1.7449430469940077e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 1.1259839999999999 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1259840000000025 Order of pole (three term test) 2.52273203902609e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2242879999999996 y[1] (closed_form) 0.6671643236859892 y[1] (numeric) 0.6671641838435699 absolute error 1.3984241931108699e-07 relative error 2.0960716025472894e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 1.2242879999999996 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.224288000000002 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3553599999999992 y[1] (closed_form) 0.5443655976215902 y[1] (numeric) 0.5443654563724056 absolute error 1.4124918457092406e-07 relative error 2.5947485511219225e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 1.3553599999999992 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.3553600000000052 Order of pole (three term test) 5.132565558798303e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4864319999999989 y[1] (closed_form) 0.4525951622028792 y[1] (numeric) 0.4525950203117714 absolute error 1.418911078077123e-07 relative error 3.135055777377234e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 1.4864319999999989 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.4864320000000049 Order of pole (three term test) 5.11594631931055e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6175039999999985 y[1] (closed_form) 0.3822163609914455 y[1] (numeric) 0.38221621878602335 absolute error 1.422054221600355e-07 relative error 3.720547749216268e-05% Desired digits 16 Estimated correct digits 12 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 1.6175039999999985 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6175040000000003 Order of pole (three term test) 4.0347395738538e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7485759999999981 y[1] (closed_form) 0.32706266681521073 y[1] (numeric) 0.32706252444656214 absolute error 1.4236864859240583e-07 relative error 4.3529470966138616e-05% Desired digits 16 Estimated correct digits 12 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 1.7485759999999981 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.7485759999999964 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8796479999999978 y[1] (closed_form) 0.28303943336383264 y[1] (numeric) 0.28303929090608837 absolute error 1.4245774426768776e-07 relative error 5.033141233171056e-05% Desired digits 16 Estimated correct digits 12 Correct digits 7 h -0.032768 Radius of convergence (given) for eq 1 1.8796479999999978 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8796480000000009 Order of pole (three term test) 2.8545683526989986e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations 40 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%