##############ECHO OF PROBLEM################# ##############temp/sing3postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; ! #BEGIN FIRST INPUT BLOCK # Digits:=16; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-2.0 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]=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 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.152559056001943e-102 estimated_step_error 7.152559056001943e-102 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 650000.0 step_error 6.201736729460424e-21 est_needed_step_err 6.201736729460424e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.68750220588339e-97 estimated_step_error 4.68750220588339e-97 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 325000.0 step_error 8.770580193070291e-21 est_needed_step_err 8.770580193070291e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.072002891296846e-92 estimated_step_error 3.072002891296846e-92 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 162500.0 step_error 1.2403473458920847e-20 est_needed_step_err 1.2403473458920847e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0132697096841825e-87 estimated_step_error 2.0132697096841825e-87 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 81250.0 step_error 1.7541160386140583e-20 est_needed_step_err 1.7541160386140583e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3194189205554354e-82 estimated_step_error 1.3194189205554354e-82 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 40625.0 step_error 2.4806946917841695e-20 est_needed_step_err 2.4806946917841695e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.646976391198815e-78 estimated_step_error 8.646976391198815e-78 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 20312.5 step_error 3.5082320772281166e-20 est_needed_step_err 3.5082320772281166e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.666925116673318e-73 estimated_step_error 5.666925116673318e-73 Double H and LOOP opt_iter 8 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 10156.25 step_error 4.961389383568339e-20 est_needed_step_err 4.961389383568339e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.713931972760191e-68 estimated_step_error 3.713931972760191e-68 Double H and LOOP opt_iter 9 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 5078.125 step_error 7.016464154456233e-20 est_needed_step_err 7.016464154456233e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.4340357673292027e-63 estimated_step_error 2.4340357673292027e-63 Double H and LOOP opt_iter 10 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 2539.0625 step_error 9.922778767136678e-20 est_needed_step_err 9.922778767136678e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5952657776289184e-58 estimated_step_error 1.5952657776289184e-58 Double H and LOOP opt_iter 11 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 1269.53125 step_error 1.4032928308912466e-19 est_needed_step_err 1.4032928308912466e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0455993593316818e-53 estimated_step_error 1.0455993593316818e-53 Double H and LOOP opt_iter 12 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 634.765625 step_error 1.9845557534273356e-19 est_needed_step_err 1.9845557534273356e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.854091796399115e-49 estimated_step_error 6.854091796399115e-49 Double H and LOOP opt_iter 13 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 317.3828125 step_error 2.8065856617824933e-19 est_needed_step_err 2.8065856617824933e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.494064264907686e-44 estimated_step_error 4.494064264907686e-44 Double H and LOOP opt_iter 14 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 158.69140625 step_error 3.969111506854671e-19 est_needed_step_err 3.969111506854671e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.948073975815616e-39 estimated_step_error 2.948073975815616e-39 Double H and LOOP opt_iter 15 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 79.345703125 step_error 5.613171323564987e-19 est_needed_step_err 5.613171323564987e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9357883308012355e-34 estimated_step_error 1.9357883308012355e-34 Double H and LOOP opt_iter 16 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 39.6728515625 step_error 7.938223013709342e-19 est_needed_step_err 7.938223013709342e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2735671124535672e-29 estimated_step_error 1.2735671124535672e-29 Double H and LOOP opt_iter 17 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000008 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.25 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 1.3 estimated_steps 19.83642578125 step_error 1.1226342647129973e-18 est_needed_step_err 1.1226342647129973e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.411814337987063e-25 estimated_step_error 8.411814337987063e-25 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.525878906250006 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] -2.0 y[1] (closed_form) 0.25 y[1] (numeric) 0.25 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 2.0 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 2.000000000000011 Order of pole (three term test) 7.640713280344897e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.9 y[1] (closed_form) 0.2770083102493075 y[1] (numeric) 0.277008301656629 absolute error 8.592678513164032e-09 relative error 3.101956943252215e-06% Desired digits 16 Estimated correct digits 14 Correct digits 8 h 0.1 Radius of convergence (given) for eq 1 1.9 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.900000000000009 Order of pole (three term test) 8.746630688723272e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7999999999999998 y[1] (closed_form) 0.308641975308642 y[1] (numeric) 0.30864195369708763 absolute error 2.1611554379408204e-08 relative error 7.002143618928257e-06% Desired digits 16 Estimated correct digits 14 Correct digits 8 h 0.1 Radius of convergence (given) for eq 1 1.7999999999999998 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.8000000000000023 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6999999999999997 y[1] (closed_form) 0.3460207612456749 y[1] (numeric) 0.3460207194545793 absolute error 4.179109558410943e-08 relative error 1.207762662380762e-05% Desired digits 16 Estimated correct digits 14 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 1.6999999999999997 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6999999999999984 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5999999999999996 y[1] (closed_form) 0.39062500000000017 y[1] (numeric) 0.39062492612474414 absolute error 7.387525602364775e-08 relative error 1.8912065542053817e-05% Desired digits 16 Estimated correct digits 14 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 1.5999999999999996 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.6000000000000039 Order of pole (three term test) 3.228584925333639e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4999999999999996 y[1] (closed_form) 0.4444444444444447 y[1] (numeric) 0.44444431807961876 absolute error 1.263648259364203e-07 relative error 2.8432085835694548e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 1.4999999999999996 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.5000000000000062 Order of pole (three term test) 3.725979779054982e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3999999999999995 y[1] (closed_form) 0.5102040816326534 y[1] (numeric) 0.5102038665750483 absolute error 2.1505760505746707e-07 relative error 4.215129059126352e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 1.3999999999999995 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.400000000000007 Order of pole (three term test) 7.524259668046792e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2999999999999994 y[1] (closed_form) 0.5917159763313615 y[1] (numeric) 0.5917156057807762 absolute error 3.705505853268676e-07 relative error 6.262304892024055e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 1.2999999999999994 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2999999999999998 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1999999999999993 y[1] (closed_form) 0.6944444444444453 y[1] (numeric) 0.6944437894714137 absolute error 6.549730315885682e-07 relative error 9.43161165487537e-05% Desired digits 16 Estimated correct digits 13 Correct digits 7 h 0.1 Radius of convergence (given) for eq 1 1.1999999999999993 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.2000000000000008 Order of pole (three term test) 2.3616202516786193e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.0999999999999992 y[1] (closed_form) 0.8264462809917367 y[1] (numeric) 0.8264450794216911 absolute error 1.2015700455725309e-06 relative error 0.00014538997551427605% Desired digits 16 Estimated correct digits 13 Correct digits 6 h 0.1 Radius of convergence (given) for eq 1 1.0999999999999992 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.1000000000000034 Order of pole (three term test) 2.7776224927074508e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9999999999999992 y[1] (closed_form) 1.0000000000000018 y[1] (numeric) 0.9999976850307339 absolute error 2.31496926783592e-06 relative error 0.0002314969267835916% Desired digits 16 Estimated correct digits 13 Correct digits 6 h 0.1 Radius of convergence (given) for eq 1 0.9999999999999992 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0000000000000024 Order of pole (three term test) 2.5469044267815667e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8999999999999992 y[1] (closed_form) 1.23456790123457 y[1] (numeric) 1.2345631547655236 absolute error 4.746469046468249e-06 relative error 0.0003844639927639275% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.1 SETTING H FOR POLE Radius of convergence (given) for eq 1 0.8999999999999992 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9000000000000015 Order of pole (three term test) 3.454919317361469e-14 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] -0.7289999999999989 y[1] (closed_form) 1.8816764231589265 y[1] (numeric) 1.8816649688486977 absolute error 1.1454310228753428e-05 relative error 0.0006087290082278932% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.08100000000000018 SETTING H FOR POLE Radius of convergence (given) for eq 1 0.7289999999999989 Order of pole (given) 2.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7290000000000006 Order of pole (three term test) 2.97445895863916e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations 14 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 108.98461538461548%