##############ECHO OF PROBLEM################# ##############temp/mult2postode.ode################# diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #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_min_h=0.00000000001 # 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 # 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 - expt(cos(x),2)/2.0) 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-11 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.9 estimated_steps 90000000000.00002 step_error 1.111111111111111e-23 est_needed_step_err 1.111111111111111e-23 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 1.0e-11 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 90000000000.00002 step_error 1.6722037283774328e-23 est_needed_step_err 1.6722037283774328e-23 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.0771477345165446e-306 estimated_step_error 4.0771477345165446e-306 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 2.0e-11 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 45000000000.00001 step_error 2.3648531917222203e-23 est_needed_step_err 2.3648531917222203e-23 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.7361275282355835e-298 estimated_step_error 2.7361275282355835e-298 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 4.0e-11 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 22500000000.000004 step_error 3.3444074567548656e-23 est_needed_step_err 3.3444074567548656e-23 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8361841017899037e-290 estimated_step_error 1.8361841017899037e-290 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 8.0e-11 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 11250000000.000002 step_error 4.7297063834444406e-23 est_needed_step_err 4.7297063834444406e-23 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.232242291659438e-282 estimated_step_error 1.232242291659438e-282 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 1.6e-10 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 5625000000.000001 step_error 6.688814913509731e-23 est_needed_step_err 6.688814913509731e-23 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.269438036597189e-275 estimated_step_error 8.269438036597189e-275 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 3.2e-10 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 2812500000.0000005 step_error 9.459412766888881e-23 est_needed_step_err 9.459412766888881e-23 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.549525925537611e-267 estimated_step_error 5.549525925537611e-267 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 6.4e-10 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 1406250000.0000002 step_error 1.3377629827019462e-22 est_needed_step_err 1.3377629827019462e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.7242238060048294e-259 estimated_step_error 3.7242238060048294e-259 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 1.28e-09 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 703125000.0000001 step_error 1.8918825533777762e-22 est_needed_step_err 1.8918825533777762e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.4992842890153958e-251 estimated_step_error 2.4992842890153958e-251 Double H and LOOP opt_iter 9 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 2.56e-09 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 351562500.00000006 step_error 2.6755259654038924e-22 est_needed_step_err 2.6755259654038924e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6772412944725907e-243 estimated_step_error 1.6772412944725907e-243 Double H and LOOP opt_iter 10 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 5.12e-09 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 175781250.00000003 step_error 3.7837651067555525e-22 est_needed_step_err 3.7837651067555525e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1255775792378169e-235 estimated_step_error 1.1255775792378169e-235 Double H and LOOP opt_iter 11 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 1.024e-08 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 87890625.00000001 step_error 5.351051930807785e-22 est_needed_step_err 5.351051930807785e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.553623268361628e-228 estimated_step_error 7.553623268361628e-228 Double H and LOOP opt_iter 12 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 2.048e-08 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 43945312.50000001 step_error 7.567530213511105e-22 est_needed_step_err 7.567530213511105e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.069150765847445e-220 estimated_step_error 5.069150765847445e-220 Double H and LOOP opt_iter 13 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 4.096e-08 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 21972656.250000004 step_error 1.070210386161557e-21 est_needed_step_err 1.070210386161557e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.401849492884454e-212 estimated_step_error 3.401849492884454e-212 Double H and LOOP opt_iter 14 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 8.192e-08 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 10986328.125000002 step_error 1.513506042702221e-21 est_needed_step_err 1.513506042702221e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.282942548962471e-204 estimated_step_error 2.282942548962471e-204 Double H and LOOP opt_iter 15 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 1.6384e-07 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 5493164.062500001 step_error 2.140420772323114e-21 est_needed_step_err 2.140420772323114e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.532056809439086e-196 estimated_step_error 1.532056809439086e-196 Double H and LOOP opt_iter 16 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 1.5049833555396894 $glob_desired_digits_correct 16 estimated_h 3.2768e-07 estimated_answer 1.5049833555396894 desired_abs_gbl_error 1.5049833555396895e-16 range 0.9 estimated_steps 2746582.0312500005 step_error 3.027012085404442e-21 est_needed_step_err 3.027012085404442e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.028145919384519e-188 estimated_step_error 1.028145919384519e-188 Double H and LOOP opt_iter 17 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735459560954814 Order of pole (three term test) 22.03946904458239 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) 1.5049833555396894 y[1] (numeric) 1.5049833555396894 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 3.2768e-07 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] 0.1900002611186727 y[1] (closed_form) 1.5178338895330346 y[1] (numeric) 1.5178338895331855 absolute error 1.509903313490213e-13 relative error 9.947750698561214e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 3.2768e-07 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] 0.2800001945598865 y[1] (closed_form) 1.538186273920425 y[1] (numeric) 1.5381862739201762 absolute error 2.489120021209601e-13 relative error 1.618217548428319e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 3.2768e-07 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! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; Iterations 761842 Total Elapsed Time 3 Minutes 0 Seconds Elapsed Time(since restart) 3 Minutes 0 Seconds Expected Time Remaining 7 Minutes 48.93260897005928 Seconds Optimized Time Remaining 7 Minutes 48.93260897005928 Seconds Expected Total Time 10 Minutes 48.93260897005928 Seconds Time to Timeout 0.0 Seconds Percent Done 27.737857138306467%