##############ECHO OF PROBLEM################# ##############temp/diff2postode.ode################# diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-1.0 x_end=1.0 $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( - 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 2.0 estimated_steps 2000000.0 step_error 1.7677669529663688e-21 est_needed_step_err 1.7677669529663688e-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 0.5403023058681398 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 2.0 estimated_steps 2000000.0 step_error 1.7677669529663688e-21 est_needed_step_err 1.7677669529663688e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4524516391245026e-258 estimated_step_error 1.4524516391245026e-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 0.5403023058681398 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 2.0 estimated_steps 1000000.0 step_error 2.5e-21 est_needed_step_err 2.5e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.981171872562365e-248 estimated_step_error 9.981171872562365e-248 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 0.5403023058681398 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 2.0 estimated_steps 500000.0 step_error 3.5355339059327375e-21 est_needed_step_err 3.5355339059327375e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.859009371655742e-237 estimated_step_error 6.859009371655742e-237 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 0.5403023058681398 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 2.0 estimated_steps 250000.0 step_error 5.0e-21 est_needed_step_err 5.0e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.713475746275112e-226 estimated_step_error 4.713475746275112e-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 0.5403023058681398 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 2.0 estimated_steps 125000.0 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 3.239076414276356e-215 estimated_step_error 3.239076414276356e-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 0.5403023058681398 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 2.0 estimated_steps 62500.0 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 2.2258771125038423e-204 estimated_step_error 2.2258771125038423e-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 0.5403023058681398 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 2.0 estimated_steps 31250.0 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 1.529612134650211e-193 estimated_step_error 1.529612134650211e-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 0.5403023058681398 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 2.0 estimated_steps 15625.0 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 1.051142870849843e-182 estimated_step_error 1.051142870849843e-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 0.4546487134128407 Order of pole (three term test) 32.708073418273806 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (closed_form) -0.5403023058681398 y[1] (numeric) -0.5403023058681398 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] -0.8999039999999867 y[1] (closed_form) -0.6216851647895049 y[1] (numeric) -0.6216851647894953 absolute error 9.547918011776346e-15 relative error 1.5358124260547792e-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] -0.7999359999999734 y[1] (closed_form) -0.6967526187101154 y[1] (numeric) -0.6967526187100959 absolute error 1.9539925233402755e-14 relative error 2.804427957454489e-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] -0.6999679999999602 y[1] (closed_form) -0.764862801858903 y[1] (numeric) -0.7648628018588776 absolute error 2.5424107263916085e-14 relative error 3.324008855199388e-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] -0.5999999999999469 y[1] (closed_form) -0.8253356149097083 y[1] (numeric) -0.8253356149096795 absolute error 2.8754776337791554e-14 relative error 3.484010118833576e-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] -0.4999039999999336 y[1] (closed_form) -0.8776285826981394 y[1] (numeric) -0.8776285826981101 absolute error 2.930988785010413e-14 relative error 3.339668787905154e-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] -0.39993599999992036 y[1] (closed_form) -0.9210859148904739 y[1] (numeric) -0.9210859148904443 absolute error 2.9531932455029164e-14 relative error 3.2062082350418746e-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] -0.2999679999999071 y[1] (closed_form) -0.9553459452831128 y[1] (numeric) -0.9553459452830861 absolute error 2.6645352591003757e-14 relative error 2.789078942822908e-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] -0.19999999999990467 y[1] (closed_form) -0.9800665778412606 y[1] (numeric) -0.9800665778412426 absolute error 1.7985612998927536e-14 relative error 1.8351419592884665e-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] -0.09990399999991036 y[1] (closed_form) -0.9950137447010389 y[1] (numeric) -0.9950137447010305 absolute error 8.326672684688674e-15 relative error 8.36839966184638e-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] 6.400000009123671e-05 y[1] (closed_form) -0.999999997952 y[1] (numeric) -0.9999999979520001 absolute error 1.1102230246251565e-16 relative error 1.1102230268988933e-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] 0.10003200000009284 y[1] (closed_form) -0.9950009700992422 y[1] (numeric) -0.995000970099252 absolute error 9.880984919163893e-15 relative error 9.930628427606815e-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] 0.20000000000008714 y[1] (closed_form) -0.9800665778412243 y[1] (numeric) -0.9800665778412422 absolute error 1.787459069646502e-14 relative error 1.823813922502803e-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] 0.30009600000008957 y[1] (closed_form) -0.9553081147835931 y[1] (numeric) -0.9553081147836199 absolute error 2.6756374893466273e-14 relative error 2.8008110136829957e-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] 0.40006400000010284 y[1] (closed_form) -0.9210360693426214 y[1] (numeric) -0.9210360693426624 absolute error 4.0967229608668276e-14 relative error 4.447950625637078e-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] 0.500032000000116 y[1] (closed_form) -0.8775672198237621 y[1] (numeric) -0.8775672198238197 absolute error 5.762057497804562e-14 relative error 6.56594431474062e-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] 0.6000000000001293 y[1] (closed_form) -0.8253356149096053 y[1] (numeric) -0.8253356149096787 absolute error 7.338574192772285e-14 relative error 8.891624280113055e-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] 0.7000960000001426 y[1] (closed_form) -0.7647803388621239 y[1] (numeric) -0.764780338862215 absolute error 9.103828801926284e-14 relative error 1.1903847862343568e-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] 0.8000640000001559 y[1] (closed_form) -0.6966607971304121 y[1] (numeric) -0.6966607971305223 absolute error 1.1024514634527804e-13 relative error 1.5824795481442974e-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] 0.9000320000001691 y[1] (closed_form) -0.6215849014911639 y[1] (numeric) -0.6215849014912959 absolute error 1.3200551762793111e-13 relative error 2.1236924724402695e-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 ) = m1 * diff ( y , x , 1 ) ; Iterations 15625 Total Elapsed Time 8 Seconds Elapsed Time(since restart) 8 Seconds Time to Timeout 2 Minutes 52.0 Seconds Percent Done 100.00640000000911%