##############ECHO OF PROBLEM################# ##############temp/sin_backpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK # ELIMINATED in preodein.rb # Digits:=32; ELIMINATED in preodein.rb max_terms=40 # ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # ELIMINATED in preodein.rb x_start=-0.1 x_end=-1.0 $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 # ELIMINATED in preodein.rb $glob_type_given_pole=3 # 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(2.0 - 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 -0.9 estimated_steps 900000.0000000001 step_error 2.6352313834736493e-21 est_needed_step_err 2.6352313834736493e-21 opt_iter 1 min_size 1.0049958347219743 $glob_desired_digits_correct 16 estimated_h -1.0e-06 estimated_answer 1.0049958347219743 desired_abs_gbl_error 1.0049958347219743e-16 range -0.9 estimated_steps 900000.0000000001 step_error 2.648396563919643e-21 est_needed_step_err 2.648396563919643e-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 min_size 1.0049958347219743 $glob_desired_digits_correct 16 estimated_h -2.0e-06 estimated_answer 1.0049958347219743 desired_abs_gbl_error 1.0049958347219743e-16 range -0.9 estimated_steps 450000.00000000006 step_error 3.7453983392374635e-21 est_needed_step_err 3.7453983392374635e-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 min_size 1.0049958347219743 $glob_desired_digits_correct 16 estimated_h -4.0e-06 estimated_answer 1.0049958347219743 desired_abs_gbl_error 1.0049958347219743e-16 range -0.9 estimated_steps 225000.00000000003 step_error 5.296793127839286e-21 est_needed_step_err 5.296793127839286e-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 min_size 1.0049958347219743 $glob_desired_digits_correct 16 estimated_h -8.0e-06 estimated_answer 1.0049958347219743 desired_abs_gbl_error 1.0049958347219743e-16 range -0.9 estimated_steps 112500.00000000001 step_error 7.490796678474927e-21 est_needed_step_err 7.490796678474927e-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 min_size 1.0049958347219743 $glob_desired_digits_correct 16 estimated_h -1.6e-05 estimated_answer 1.0049958347219743 desired_abs_gbl_error 1.0049958347219743e-16 range -0.9 estimated_steps 56250.00000000001 step_error 1.0593586255678572e-20 est_needed_step_err 1.0593586255678572e-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 min_size 1.0049958347219743 $glob_desired_digits_correct 16 estimated_h -3.2e-05 estimated_answer 1.0049958347219743 desired_abs_gbl_error 1.0049958347219743e-16 range -0.9 estimated_steps 28125.000000000004 step_error 1.4981593356949854e-20 est_needed_step_err 1.4981593356949854e-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 min_size 1.0049958347219743 $glob_desired_digits_correct 16 estimated_h -6.4e-05 estimated_answer 1.0049958347219743 desired_abs_gbl_error 1.0049958347219743e-16 range -0.9 estimated_steps 14062.500000000002 step_error 2.1187172511357145e-20 est_needed_step_err 2.1187172511357145e-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 min_size 1.0049958347219743 $glob_desired_digits_correct 16 estimated_h -0.000128 estimated_answer 1.0049958347219743 desired_abs_gbl_error 1.0049958347219743e-16 range -0.9 estimated_steps 7031.250000000001 step_error 2.996318671389971e-20 est_needed_step_err 2.996318671389971e-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 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] -0.10012800000000001 y[1] (closed_form) 1.0050086215503442 y[1] (numeric) 1.0050086215503442 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) 1.019952498930631 y[1] (numeric) 1.0199524989306308 absolute error 2.220446049250313e-16 relative error 2.177009274038094e-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) 1.0446824261241354 y[1] (numeric) 1.0446824261241354 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] -0.40003200000001005 y[1] (closed_form) 1.0789514678556538 y[1] (numeric) 1.0789514678556509 absolute error 2.886579864025407e-15 relative error 2.675356538290177e-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] -0.5001280000000233 y[1] (closed_form) 1.1224788117675686 y[1] (numeric) 1.1224788117675617 absolute error 6.8833827526759706e-15 relative error 6.132305287648771e-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) 1.1747185945708516 y[1] (numeric) 1.1747185945708378 absolute error 1.3766765505351941e-14 relative error 1.1719202853327794e-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) 1.2351990442138956 y[1] (numeric) 1.2351990442138738 absolute error 2.1760371282653068e-14 relative error 1.7616894527717017e-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) 1.3033162464044987 y[1] (numeric) 1.3033162464044676 absolute error 3.108624468950438e-14 relative error 2.3851651335785177e-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] -0.9001280000000764 y[1] (closed_form) 1.3784903026657829 y[1] (numeric) 1.3784903026657425 absolute error 4.04121180963557e-14 relative error 2.931621500579658e-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 ) = sin ( x ) ; Iterations 7032 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Expected Time Remaining 0.0 Seconds Optimized Time Remaining 0.0 Seconds Expected Total Time 1.0 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 0.0%