##############ECHO OF PROBLEM################# ##############temp/h3sinpostode.ode################# diff ( y , x , 3 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; 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) $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(1.0 + cos(x)) end def exact_soln_yp (x) return(-sin(x)) end def exact_soln_ypp (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 1.9950041652780257 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.9950041652780257 desired_abs_gbl_error 1.9950041652780256e-16 range 1.4 estimated_steps 1400000.0 step_error 4.21521564621459e-21 est_needed_step_err 4.21521564621459e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.6747903585133234e-258 estimated_step_error 2.6747903585133234e-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 1.9950041652780257 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.9950041652780257 desired_abs_gbl_error 1.9950041652780256e-16 range 1.4 estimated_steps 700000.0 step_error 5.961215135203943e-21 est_needed_step_err 5.961215135203943e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8381019356630986e-247 estimated_step_error 1.8381019356630986e-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 1.9950041652780257 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.9950041652780257 desired_abs_gbl_error 1.9950041652780256e-16 range 1.4 estimated_steps 350000.0 step_error 8.43043129242918e-21 est_needed_step_err 8.43043129242918e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.263134028636665e-236 estimated_step_error 1.263134028636665e-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 1.9950041652780257 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.9950041652780257 desired_abs_gbl_error 1.9950041652780256e-16 range 1.4 estimated_steps 175000.0 step_error 1.1922430270407885e-20 est_needed_step_err 1.1922430270407885e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.680190902457671e-226 estimated_step_error 8.680190902457671e-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 1.9950041652780257 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.9950041652780257 desired_abs_gbl_error 1.9950041652780256e-16 range 1.4 estimated_steps 87500.0 step_error 1.686086258485836e-20 est_needed_step_err 1.686086258485836e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.964981703152478e-215 estimated_step_error 5.964981703152478e-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 1.9950041652780257 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.9950041652780257 desired_abs_gbl_error 1.9950041652780256e-16 range 1.4 estimated_steps 43750.0 step_error 2.384486054081577e-20 est_needed_step_err 2.384486054081577e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.0991041248780636e-204 estimated_step_error 4.0991041248780636e-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 1.9950041652780257 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.9950041652780257 desired_abs_gbl_error 1.9950041652780256e-16 range 1.4 estimated_steps 21875.0 step_error 3.372172516971672e-20 est_needed_step_err 3.372172516971672e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.816882783259633e-193 estimated_step_error 2.816882783259633e-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 1.9950041652780257 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.9950041652780257 desired_abs_gbl_error 1.9950041652780256e-16 range 1.4 estimated_steps 10937.5 step_error 4.768972108163154e-20 est_needed_step_err 4.768972108163154e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.935746940941988e-182 estimated_step_error 1.935746940941988e-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) 1.9950041652780257 y[1] (numeric) 1.9950041652780257 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) 1.980047501069369 y[1] (numeric) 1.980047501069369 absolute error 0.0 relative error 0.0% 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) 1.9553175738758646 y[1] (numeric) 1.9553175738758635 absolute error 1.1102230246251565e-15 relative error 5.6779678117680553e-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) 1.9210485321443462 y[1] (numeric) 1.921048532144348 absolute error 1.7763568394002505e-15 relative error 9.246808759263435e-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] 0.5000000000000233 y[1] (closed_form) 1.8775825618903617 y[1] (numeric) 1.8775825618903679 absolute error 6.217248937900877e-15 relative error 3.3113052198574494e-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] 0.6000960000000366 y[1] (closed_form) 1.8252814054291484 y[1] (numeric) 1.8252814054291646 absolute error 1.6209256159527285e-14 relative error 8.880414883597781e-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] 0.7000640000000499 y[1] (closed_form) 1.7648009557861044 y[1] (numeric) 1.7648009557861324 absolute error 2.7977620220553945e-14 relative error 1.5853130705095141e-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) 1.6966837535955013 y[1] (numeric) 1.6966837535955415 absolute error 4.0190073491430667e-14 relative error 2.3687427551694586e-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) 1.6216099682706044 y[1] (numeric) 1.6216099682706582 absolute error 5.3734794391857577e-14 relative error 3.3136694669658468e-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] 1.0000960000000896 y[1] (closed_form) 1.5402215221639337 y[1] (numeric) 1.5402215221640032 absolute error 6.94999613415348e-14 relative error 4.5123354232767016e-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] 1.1000640000000161 y[1] (closed_form) 1.4535390832255932 y[1] (numeric) 1.453539083225604 absolute error 1.0880185641326534e-14 relative error 7.485306564431677e-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] 1.2000319999999427 y[1] (closed_form) 1.362327929040454 y[1] (numeric) 1.3623279290403971 absolute error 5.684341886080802e-14 relative error 4.172520995062127e-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] 1.2999999999998693 y[1] (closed_form) 1.2674988286247133 y[1] (numeric) 1.2674988286245858 absolute error 1.2745360322696797e-13 relative error 1.0055520395648823e-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) 1.1698725389433 y[1] (numeric) 1.1698725389430997 absolute error 2.0028423364237824e-13 relative error 1.7120175658049648e-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 Finished! diff ( y , x , 3 ) = sin ( x ) ; Iterations 10938 Total Elapsed Time 4 Seconds Elapsed Time(since restart) 4 Seconds Time to Timeout 2 Minutes 56.0 Seconds Percent Done 100.01371428569445%