##############ECHO OF PROBLEM################# ##############temp/add_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 + 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=1.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.001 # 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(2.0 - cos(x) + 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 0.9 estimated_steps 900000.0000000001 step_error 2.6352313834736493e-21 est_needed_step_err 2.6352313834736493e-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 1.1049958347219744 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.1049958347219744 desired_abs_gbl_error 1.1049958347219744e-16 range 0.9 estimated_steps 900000.0000000001 step_error 2.9119197022670088e-21 est_needed_step_err 2.9119197022670088e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.674790358513323e-258 estimated_step_error 2.674790358513323e-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 1.1049958347219744 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.1049958347219744 desired_abs_gbl_error 1.1049958347219744e-16 range 0.9 estimated_steps 450000.00000000006 step_error 4.118076335487429e-21 est_needed_step_err 4.118076335487429e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8381019356630983e-247 estimated_step_error 1.8381019356630983e-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 1.1049958347219744 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.1049958347219744 desired_abs_gbl_error 1.1049958347219744e-16 range 0.9 estimated_steps 225000.00000000003 step_error 5.8238394045340175e-21 est_needed_step_err 5.8238394045340175e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2631340286366648e-236 estimated_step_error 1.2631340286366648e-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 1.1049958347219744 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.1049958347219744 desired_abs_gbl_error 1.1049958347219744e-16 range 0.9 estimated_steps 112500.00000000001 step_error 8.236152670974858e-21 est_needed_step_err 8.236152670974858e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.68019090245767e-226 estimated_step_error 8.68019090245767e-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 1.1049958347219744 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.1049958347219744 desired_abs_gbl_error 1.1049958347219744e-16 range 0.9 estimated_steps 56250.00000000001 step_error 1.1647678809068035e-20 est_needed_step_err 1.1647678809068035e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.964981703152477e-215 estimated_step_error 5.964981703152477e-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 1.1049958347219744 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.1049958347219744 desired_abs_gbl_error 1.1049958347219744e-16 range 0.9 estimated_steps 28125.000000000004 step_error 1.6472305341949716e-20 est_needed_step_err 1.6472305341949716e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.099104124878063e-204 estimated_step_error 4.099104124878063e-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 1.1049958347219744 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.1049958347219744 desired_abs_gbl_error 1.1049958347219744e-16 range 0.9 estimated_steps 14062.500000000002 step_error 2.329535761813607e-20 est_needed_step_err 2.329535761813607e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.8168827832596326e-193 estimated_step_error 2.8168827832596326e-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 1.1049958347219744 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.1049958347219744 desired_abs_gbl_error 1.1049958347219744e-16 range 0.9 estimated_steps 7031.250000000001 step_error 3.294461068389943e-20 est_needed_step_err 3.294461068389943e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9357469409419875e-182 estimated_step_error 1.9357469409419875e-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) 1.1049958347219744 y[1] (numeric) 1.1049958347219744 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] 0.19011199999999515 y[1] (closed_form) 1.2081289232380477 y[1] (numeric) 1.2081289232380532 absolute error 5.551115123125783e-15 relative error 4.594803597820993e-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] 0.2800959999999941 y[1] (closed_form) 1.3190670962599864 y[1] (numeric) 1.3190670962599942 absolute error 7.771561172376096e-15 relative error 5.891710281009338e-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] 0.37008000000000607 y[1] (closed_form) 1.4377815866119477 y[1] (numeric) 1.437781586611937 absolute error 1.0658141036401503e-14 relative error 7.412906894653464e-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] 0.460064000000018 y[1] (closed_form) 1.5640399169884427 y[1] (numeric) 1.5640399169884138 absolute error 2.886579864025407e-14 relative error 1.845592195360022e-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] 0.55004800000003 y[1] (closed_form) 1.6975485679096272 y[1] (numeric) 1.6975485679095825 absolute error 4.463096558993129e-14 relative error 2.6291421897218628e-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] 0.6400320000000419 y[1] (closed_form) 1.8379553527805677 y[1] (numeric) 1.837955352780508 absolute error 5.972999872483342e-14 relative error 3.249806837498547e-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] 0.7300160000000538 y[1] (closed_form) 1.984852267664761 y[1] (numeric) 1.9848522676646831 absolute error 7.793765632868599e-14 relative error 3.926622529967029e-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] 0.8200000000000658 y[1] (closed_form) 2.1377787927125 y[1] (numeric) 2.1377787927124023 absolute error 9.769962616701378e-14 relative error 4.57014666344634e-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] 0.9101120000000777 y[1] (closed_form) 2.2964546787794013 y[1] (numeric) 2.2964546787792797 absolute error 1.2168044349891716e-13 relative error 5.298621593681616e-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 Finished! diff ( y , x , 1 ) = 1.0 + sin ( x ) ; Iterations 7032 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.02488888889884%