##############ECHO OF PROBLEM################# ##############temp/h5h3postode.ode################# diff ( y , x , 5 ) = m1 * diff ( y , x , 3 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=1.5 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $array_y_init[0 + 1] = exact_soln_y(x_start) $array_y_init[1 + 1] = exact_soln_yp(x_start) $array_y_init[2 + 1] = exact_soln_ypp(x_start) $array_y_init[3 + 1] = exact_soln_yppp(x_start) $array_y_init[4 + 1] = exact_soln_ypppp(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=3 #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(cos(x)) end def exact_soln_yp (x) return(-sin(x)) end def exact_soln_ypp (x) return(-cos(x)) end def exact_soln_yppp (x) return(sin(x)) end def exact_soln_ypppp (x) return(cos(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 1.4 estimated_steps 1400000.0 step_error 2.1128856368212915e-21 est_needed_step_err 2.1128856368212915e-21 opt_iter 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.9950041652780258 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 1.4 estimated_steps 1400000.0 step_error 2.1128856368212915e-21 est_needed_step_err 2.1128856368212915e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.674790358513321e-258 estimated_step_error 2.674790358513321e-258 Double H and LOOP opt_iter 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.9950041652780258 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 1.4 estimated_steps 700000.0 step_error 2.988071523335984e-21 est_needed_step_err 2.988071523335984e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.838101935663097e-247 estimated_step_error 1.838101935663097e-247 Double H and LOOP opt_iter 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.9950041652780258 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 1.4 estimated_steps 350000.0 step_error 4.225771273642583e-21 est_needed_step_err 4.225771273642583e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.263134028636664e-236 estimated_step_error 1.263134028636664e-236 Double H and LOOP opt_iter 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.9950041652780258 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 1.4 estimated_steps 175000.0 step_error 5.976143046671968e-21 est_needed_step_err 5.976143046671968e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.680190902457664e-226 estimated_step_error 8.680190902457664e-226 Double H and LOOP opt_iter 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.9950041652780258 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 1.4 estimated_steps 87500.0 step_error 8.451542547285166e-21 est_needed_step_err 8.451542547285166e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.964981703152473e-215 estimated_step_error 5.964981703152473e-215 Double H and LOOP opt_iter 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.9950041652780258 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 1.4 estimated_steps 43750.0 step_error 1.1952286093343936e-20 est_needed_step_err 1.1952286093343936e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.09910412487806e-204 estimated_step_error 4.09910412487806e-204 Double H and LOOP opt_iter 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.9950041652780258 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 1.4 estimated_steps 21875.0 step_error 1.6903085094570332e-20 est_needed_step_err 1.6903085094570332e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.8168827832596306e-193 estimated_step_error 2.8168827832596306e-193 Double H and LOOP opt_iter 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.9950041652780258 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 1.4 estimated_steps 10937.5 step_error 2.3904572186687872e-20 est_needed_step_err 2.3904572186687872e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9357469409419862e-182 estimated_step_error 1.9357469409419862e-182 Double H and LOOP opt_iter 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09933466539749951 Order of pole (three term test) 32.00996671107996 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 0.9950041652780258 y[1] (numeric) 0.9950041652780258 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2000959999999943 y[1] (closed_form) 0.980047501069369 y[1] (numeric) 0.9800475010693684 absolute error 5.551115123125783e-16 relative error 5.664128643834854e-14% Desired digits 16 Estimated correct digits 12 Correct digits 16 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000639999999968 y[1] (closed_form) 0.9553175738758645 y[1] (numeric) 0.955317573875865 absolute error 5.551115123125783e-16 relative error 5.810753695866903e-14% Desired digits 16 Estimated correct digits 12 Correct digits 16 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40003200000001005 y[1] (closed_form) 0.9210485321443462 y[1] (numeric) 0.921048532144352 absolute error 5.773159728050814e-15 relative error 6.268029888294798e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5000000000000233 y[1] (closed_form) 0.8775825618903615 y[1] (numeric) 0.8775825618903756 absolute error 1.4099832412739488e-14 relative error 1.6066673410610696e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6000960000000366 y[1] (closed_form) 0.8252814054291484 y[1] (numeric) 0.82528140542917 absolute error 2.1538326677728037e-14 relative error 2.609816062259158e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000640000000499 y[1] (closed_form) 0.7648009557861044 y[1] (numeric) 0.7648009557861384 absolute error 3.397282455352979e-14 relative error 4.442047868338587e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000320000000631 y[1] (closed_form) 0.6966837535955014 y[1] (numeric) 0.6966837535955501 absolute error 4.873879078104437e-14 relative error 6.995827092207808e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000000000000764 y[1] (closed_form) 0.6216099682706046 y[1] (numeric) 0.6216099682706696 absolute error 6.505906924303417e-14 relative error 1.0466220389617707e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0000960000000896 y[1] (closed_form) 0.5402215221639338 y[1] (numeric) 0.5402215221640169 absolute error 8.304468224196171e-14 relative error 1.537233872306947e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1000640000000161 y[1] (closed_form) 0.45353908322559316 y[1] (numeric) 0.45353908322561753 absolute error 2.4369395390522186e-14 relative error 5.3731632601992754e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2000319999999427 y[1] (closed_form) 0.36232792904045397 y[1] (numeric) 0.36232792904041405 absolute error 3.991251773527438e-14 relative error 1.101557857849212e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2999999999998693 y[1] (closed_form) 0.26749882862471336 y[1] (numeric) 0.2674988286246064 absolute error 1.0696998842263383e-13 relative error 3.9988955829300864e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4000959999997957 y[1] (closed_form) 0.16987253894330007 y[1] (numeric) 0.16987253894312515 absolute error 1.7491563752969341e-13 relative error 1.0296875446600384e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 5 ) = m1 * diff ( y , x , 3 ) ; Iterations 10938 Total Elapsed Time 8 Seconds Elapsed Time(since restart) 8 Seconds Time to Timeout 2 Minutes 52.0 Seconds Percent Done 100.01371428569445%