##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.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=0.5 $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]=1.0 # 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(1.0/(1.0 - 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 0.5 estimated_steps 500000.0 step_error 7.071067811865475e-21 est_needed_step_err 7.071067811865475e-21 opt_iter 1 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 1.0000005000002499e-96 estimated_step_error 1.0000005000002499e-96 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 6.553606553606554e-92 estimated_step_error 6.553606553606554e-92 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 4.294975885951771e-87 estimated_step_error 4.294975885951771e-87 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 2.814761026150664e-82 estimated_step_error 2.814761026150664e-82 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 1.8446891648842738e-77 estimated_step_error 1.8446891648842738e-77 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 1.208945162737233e-72 estimated_step_error 1.208945162737233e-72 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 7.923069789659704e-68 estimated_step_error 7.923069789659704e-68 Double H and LOOP opt_iter 8 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 5.192629186802782e-63 estimated_step_error 5.192629186802782e-63 Double H and LOOP opt_iter 9 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 3.4032592863980424e-58 estimated_step_error 3.4032592863980424e-58 Double H and LOOP opt_iter 10 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 2.2306455651177226e-53 estimated_step_error 2.2306455651177226e-53 Double H and LOOP opt_iter 11 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 1.4622503094892607e-48 estimated_step_error 1.4622503094892607e-48 Double H and LOOP opt_iter 12 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 9.587915155520526e-44 estimated_step_error 9.587915155520526e-44 Double H and LOOP opt_iter 13 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 6.289983621733564e-39 estimated_step_error 6.289983621733564e-39 Double H and LOOP opt_iter 14 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 4.130680660128981e-34 estimated_step_error 4.130680660128981e-34 Double H and LOOP opt_iter 15 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 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 0.5 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 2.718262662302969e-29 estimated_step_error 2.718262662302969e-29 Double H and LOOP opt_iter 16 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9999999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.0000000000000087 Order of pole (three term test) 1.0000000000001303 NO COMPLEX POLE (six term test) for Equation 1 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 0.5 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 1.796277142160798e-24 estimated_step_error 1.796277142160798e-24 Double H and LOOP opt_iter 17 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7629394531249999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7629394531250066 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) 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 0.05 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 1.0000000000000002 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 1.000000000000002 Order of pole (three term test) 1.000000000000033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05 y[1] (closed_form) 1.0526315789473684 y[1] (numeric) 1.0526315789473684 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.95 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.9499999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.9499999999999977 Order of pole (three term test) 0.9999999999999715 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 1.1111111111111112 y[1] (numeric) 1.1111111111111112 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.9 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8999999999999999 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.9000000000000086 Order of pole (three term test) 1.000000000000121 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000002 y[1] (closed_form) 1.1764705882352942 y[1] (numeric) 1.1764705882352942 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.85 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8500000000000002 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8500000000000091 Order of pole (three term test) 1.0000000000001 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2 y[1] (closed_form) 1.25 y[1] (numeric) 1.25 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.8 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.8 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.8 Order of pole (three term test) 1.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25 y[1] (closed_form) 1.3333333333333333 y[1] (numeric) 1.3333333333333333 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.75 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7500000000000002 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7499999999999983 Order of pole (three term test) 0.999999999999972 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3 y[1] (closed_form) 1.4285714285714286 y[1] (numeric) 1.4285714285714286 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.7 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.7 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.7000000000000003 Order of pole (three term test) 1.0000000000000124 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35 y[1] (closed_form) 1.5384615384615383 y[1] (numeric) 1.5384615384615385 absolute error 2.220446049250313e-16 relative error 1.4432899320127035e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.65 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.6500000000000002 Order of pole (ratio test) 0.9999999999999999 Radius of convergence (three term test) for eq 1 0.6499999999999931 Order of pole (three term test) 0.9999999999998542 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39999999999999997 y[1] (closed_form) 1.6666666666666665 y[1] (numeric) 1.6666666666666667 absolute error 2.220446049250313e-16 relative error 1.332267629550188e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.6000000000000001 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5999999999999999 Order of pole (ratio test) 0.9999999999999997 Radius of convergence (three term test) for eq 1 0.5999999999999994 Order of pole (three term test) 1.0000000000000027 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.44999999999999996 y[1] (closed_form) 1.8181818181818181 y[1] (numeric) 1.8181818181818183 absolute error 2.220446049250313e-16 relative error 1.2212453270876722e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.55 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.55 Order of pole (ratio test) 0.9999999999999984 Radius of convergence (three term test) for eq 1 0.5500000000000014 Order of pole (three term test) 1.0000000000000457 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.49999999999999994 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 13 Correct digits 16 h 0.05 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5000000000000001 Order of pole (ratio test) 0.999999999999992 Radius of convergence (three term test) for eq 1 0.500000000000001 Order of pole (three term test) 1.000000000000033 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 120.0%