##############ECHO OF PROBLEM################# ##############temp/nonlinear2postode.ode################# diff ( y , x , 1 ) = y * y ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb x_start=0.0 x_end=0.2 $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]=0.5 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #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(2.0/(1.0 - 2.0*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 0.2 estimated_steps 200000.00000000003 step_error 1.1180339887498948e-20 est_needed_step_err 1.1180339887498948e-20 opt_iter 1 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 200000.00000000003 step_error 2.2360679774997895e-20 est_needed_step_err 2.2360679774997895e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3107213107213108e-91 estimated_step_error 1.3107213107213108e-91 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 100000.00000000001 step_error 3.162277660168379e-20 est_needed_step_err 3.162277660168379e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.589951771903542e-87 estimated_step_error 8.589951771903542e-87 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 50000.00000000001 step_error 4.472135954999579e-20 est_needed_step_err 4.472135954999579e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.629522052301328e-82 estimated_step_error 5.629522052301328e-82 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 25000.000000000004 step_error 6.324555320336758e-20 est_needed_step_err 6.324555320336758e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.6893783297685475e-77 estimated_step_error 3.6893783297685475e-77 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 12500.000000000002 step_error 8.944271909999158e-20 est_needed_step_err 8.944271909999158e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.417890325474466e-72 estimated_step_error 2.417890325474466e-72 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 6250.000000000001 step_error 1.2649110640673517e-19 est_needed_step_err 1.2649110640673517e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5846139579319407e-67 estimated_step_error 1.5846139579319407e-67 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 3125.0000000000005 step_error 1.7888543819998316e-19 est_needed_step_err 1.7888543819998316e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0385258373605564e-62 estimated_step_error 1.0385258373605564e-62 Double H and LOOP opt_iter 8 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 1562.5000000000002 step_error 2.5298221281347034e-19 est_needed_step_err 2.5298221281347034e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.806518572796085e-58 estimated_step_error 6.806518572796085e-58 Double H and LOOP opt_iter 9 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 781.2500000000001 step_error 3.5777087639996633e-19 est_needed_step_err 3.5777087639996633e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.461291130235445e-53 estimated_step_error 4.461291130235445e-53 Double H and LOOP opt_iter 10 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 390.62500000000006 step_error 5.059644256269407e-19 est_needed_step_err 5.059644256269407e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.9245006189785214e-48 estimated_step_error 2.9245006189785214e-48 Double H and LOOP opt_iter 11 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 195.31250000000003 step_error 7.1554175279993265e-19 est_needed_step_err 7.1554175279993265e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.917583031104105e-43 estimated_step_error 1.917583031104105e-43 Double H and LOOP opt_iter 12 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 97.65625000000001 step_error 1.0119288512538813e-18 est_needed_step_err 1.0119288512538813e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2579967243467127e-38 estimated_step_error 1.2579967243467127e-38 Double H and LOOP opt_iter 13 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 48.82812500000001 step_error 1.4310835055998653e-18 est_needed_step_err 1.4310835055998653e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.261361320257963e-34 estimated_step_error 8.261361320257963e-34 Double H and LOOP opt_iter 14 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 24.414062500000004 step_error 2.0238577025077627e-18 est_needed_step_err 2.0238577025077627e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.436525324605938e-29 estimated_step_error 5.436525324605938e-29 Double H and LOOP opt_iter 15 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.5000000000000043 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 min_size 2.0 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 2.0 desired_abs_gbl_error 2.0e-16 range 0.2 estimated_steps 12.207031250000002 step_error 2.8621670111997306e-18 est_needed_step_err 2.8621670111997306e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.592554284321596e-24 estimated_step_error 3.592554284321596e-24 Double H and LOOP opt_iter 16 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.30517578124999994 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.30517578125000266 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 2.0 y[1] (numeric) 2.0 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4999999999999964 Order of pole (three term test) 0.9999999999998763 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.02 y[1] (closed_form) 2.0833333333333335 y[1] (numeric) 2.0833333333333335 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.48 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4799999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4800000000000044 Order of pole (three term test) 1.000000000000155 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04 y[1] (closed_form) 2.1739130434782608 y[1] (numeric) 2.173913043478261 absolute error 4.440892098500626e-16 relative error 2.042810365310288e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.46 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.45999999999999974 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4599999999999997 Order of pole (three term test) 0.9999999999999871 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.06 y[1] (closed_form) 2.272727272727273 y[1] (numeric) 2.272727272727273 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.44 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.43999999999999995 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.43999999999999906 Order of pole (three term test) 0.9999999999999579 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08 y[1] (closed_form) 2.380952380952381 y[1] (numeric) 2.3809523809523814 absolute error 4.440892098500626e-16 relative error 1.865174681370263e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.42 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4199999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.42000000000000287 Order of pole (three term test) 1.0000000000000524 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 2.5 y[1] (numeric) 2.5000000000000004 absolute error 4.440892098500626e-16 relative error 1.7763568394002505e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.4 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.39999999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.40000000000000213 Order of pole (three term test) 1.00000000000011 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12000000000000001 y[1] (closed_form) 2.6315789473684212 y[1] (numeric) 2.6315789473684217 absolute error 4.440892098500626e-16 relative error 1.687538997430238e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.38 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.38000000000000006 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.38000000000000334 Order of pole (three term test) 1.0000000000001372 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14 y[1] (closed_form) 2.7777777777777777 y[1] (numeric) 2.7777777777777786 absolute error 8.881784197001252e-16 relative error 3.197442310920451e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.36 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.3599999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.35999999999999854 Order of pole (three term test) 0.9999999999999281 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16 y[1] (closed_form) 2.9411764705882355 y[1] (numeric) 2.9411764705882364 absolute error 8.881784197001252e-16 relative error 3.019806626980426e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.33999999999999997 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.33999999999999986 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.34000000000000086 Order of pole (three term test) 1.0000000000000342 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18 y[1] (closed_form) 3.125 y[1] (numeric) 3.1250000000000013 absolute error 1.3322676295501878e-15 relative error 4.263256414560601e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.32 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.3199999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.32000000000000406 Order of pole (three term test) 1.0000000000001388 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19999999999999998 y[1] (closed_form) 3.333333333333333 y[1] (numeric) 3.333333333333335 absolute error 1.7763568394002505e-15 relative error 5.329070518200752e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.02 Radius of convergence (given) for eq 1 0.30000000000000004 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.29999999999999977 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.3 Order of pole (three term test) 0.9999999999999857 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y ; Iterations 11 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 119.99999999999997%