##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! #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=1.4 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) $array_y2_init[1 + 1] = exact_soln_y2p(x_start) $array_y2_init[2 + 1] = exact_soln_y2pp(x_start) $array_y2_init[3 + 1] = exact_soln_y2ppp(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_y1 (x) return(1.0 + sin(x)) end def exact_soln_y2 (x) return(1.0 + sin(x)) end def exact_soln_y2p (x) return( cos(x)) end def exact_soln_y2pp (x) return( -sin(x)) end def exact_soln_y2ppp (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 1.2999999999999998 estimated_steps 1299999.9999999998 step_error 2.1926450482675736e-21 est_needed_step_err 2.1926450482675736e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 1.2999999999999998 estimated_steps 1299999.9999999998 step_error 2.4115442949298748e-21 est_needed_step_err 2.4115442949298748e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.683742500284562e-259 estimated_step_error 2.683742500284562e-259 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 1.2999999999999998 estimated_steps 649999.9999999999 step_error 3.410438648153292e-21 est_needed_step_err 3.410438648153292e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8442540515293488e-248 estimated_step_error 1.8442540515293488e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 1.2999999999999998 estimated_steps 324999.99999999994 step_error 4.8230885898597495e-21 est_needed_step_err 4.8230885898597495e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2673620752810252e-237 estimated_step_error 1.2673620752810252e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 1.2999999999999998 estimated_steps 162499.99999999997 step_error 6.820877296306584e-21 est_needed_step_err 6.820877296306584e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.709250556831444e-227 estimated_step_error 8.709250556831444e-227 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 1.2999999999999998 estimated_steps 81249.99999999999 step_error 9.646177179719499e-21 est_needed_step_err 9.646177179719499e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.984957858910743e-216 estimated_step_error 5.984957858910743e-216 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 1.2999999999999998 estimated_steps 40624.99999999999 step_error 1.3641754592613167e-20 est_needed_step_err 1.3641754592613167e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.112840586441793e-205 estimated_step_error 4.112840586441793e-205 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 1.2999999999999998 estimated_steps 20312.499999999996 step_error 1.9292354359438998e-20 est_needed_step_err 1.9292354359438998e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.82633471110443e-194 estimated_step_error 2.82633471110443e-194 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 1.0998334166468282 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0998334166468282 desired_abs_gbl_error 1.0998334166468282e-16 range 1.2999999999999998 estimated_steps 10156.249999999998 step_error 2.7283509185226335e-20 est_needed_step_err 2.7283509185226335e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.942259165876972e-183 estimated_step_error 1.942259165876972e-183 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 0.09933466539752886 Order of pole (three term test) 32.99003328892069 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.09933466539752886 Order of pole (three term test) 32.99003328892069 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y2[1] (closed_form) 1.0998334166468282 y2[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.000128 y1[1] (closed_form) 1.0998334166468282 y1[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2000959999999943 y2[1] (closed_form) 1.1987634162709155 y2[1] (numeric) 1.1987634162709222 absolute error 6.661338147750939e-15 relative error 5.556841372814721e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 y1[1] (closed_form) 1.1987634162709155 y1[1] (numeric) 1.1987634162709224 absolute error 6.8833827526759706e-15 relative error 5.742069418575212e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3000639999999968 y2[1] (closed_form) 1.2955813475913733 y2[1] (numeric) 1.2955813475913764 absolute error 3.1086244689504383e-15 relative error 2.399405081533251e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 y1[1] (closed_form) 1.2955813475913733 y1[1] (numeric) 1.2955813475913767 absolute error 3.3306690738754696e-15 relative error 2.570791158785626e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.40003200000001005 y2[1] (closed_form) 1.3894478160610806 y2[1] (numeric) 1.389447816061072 absolute error 8.659739592076221e-15 relative error 6.232504374741869e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 y1[1] (closed_form) 1.3894478160610806 y1[1] (numeric) 1.3894478160610721 absolute error 8.43769498715119e-15 relative error 6.072696570261309e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5000000000000233 y2[1] (closed_form) 1.4794255386042234 y2[1] (numeric) 1.4794255386042048 absolute error 1.865174681370263e-14 relative error 1.2607425197823596e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 y1[1] (closed_form) 1.4794255386042234 y1[1] (numeric) 1.4794255386042054 absolute error 1.7985612998927536e-14 relative error 1.2157160012187037e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6000960000000366 y2[1] (closed_form) 1.5647217030121028 y2[1] (numeric) 1.5647217030120733 absolute error 2.9531932455029164e-14 relative error 1.887360058864138e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 y1[1] (closed_form) 1.5647217030121028 y1[1] (numeric) 1.564721703012074 absolute error 2.886579864025407e-14 relative error 1.8447880274611874e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7000640000000499 y2[1] (closed_form) 1.6442666358183242 y2[1] (numeric) 1.6442666358182876 absolute error 3.6637359812630166e-14 relative error 2.2281884832137556e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 y1[1] (closed_form) 1.6442666358183242 y1[1] (numeric) 1.6442666358182885 absolute error 3.574918139293004e-14 relative error 2.174171792711604e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8000320000000631 y2[1] (closed_form) 1.7173783851469757 y2[1] (numeric) 1.717378385146931 absolute error 4.463096558993129e-14 relative error 2.5987846345295486e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 y1[1] (closed_form) 1.7173783851469757 y1[1] (numeric) 1.7173783851469324 absolute error 4.3298697960381105e-14 relative error 2.521208973797323e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9000000000000764 y2[1] (closed_form) 1.7833269096275308 y2[1] (numeric) 1.7833269096274793 absolute error 5.1514348342607263e-14 relative error 2.8886654524473393e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 y1[1] (closed_form) 1.7833269096275308 y1[1] (numeric) 1.7833269096274826 absolute error 4.8183679268731794e-14 relative error 2.7018982895735886e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0000960000000896 y2[1] (closed_form) 1.8415228499517302 y2[1] (numeric) 1.8415228499516756 absolute error 5.46229728115577e-14 relative error 2.9661849057691286e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 y1[1] (closed_form) 1.8415228499517302 y1[1] (numeric) 1.8415228499516811 absolute error 4.907185768843192e-14 relative error 2.6647433503047863e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1000640000000161 y2[1] (closed_form) 1.8912363883880015 y2[1] (numeric) 1.8912363883879841 absolute error 1.7319479184152442e-14 relative error 9.157754837254759e-13% Desired digits 16 Estimated correct digits 11 Correct digits 15 h 0.000128 y1[1] (closed_form) 1.8912363883880015 y1[1] (numeric) 1.8912363883879935 absolute error 7.993605777301127e-15 relative error 4.226656078732966e-13% Desired digits 16 Estimated correct digits 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2000319999999427 y2[1] (closed_form) 1.9320506809381428 y2[1] (numeric) 1.9320506809381484 absolute error 5.551115123125783e-15 relative error 2.873172623210037e-13% Desired digits 16 Estimated correct digits 11 Correct digits 15 h 0.000128 y1[1] (closed_form) 1.9320506809381428 y1[1] (numeric) 1.932050680938162 absolute error 1.9095836023552692e-14 relative error 9.883713823842528e-13% Desired digits 16 Estimated correct digits 11 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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2999999999998693 y2[1] (closed_form) 1.963558185417158 y2[1] (numeric) 1.9635581854171742 absolute error 1.6209256159527285e-14 relative error 8.25504244280066e-13% Desired digits 16 Estimated correct digits 11 Correct digits 15 h 0.000128 y1[1] (closed_form) 1.963558185417158 y1[1] (numeric) 1.9635581854171942 absolute error 3.6193270602780103e-14 relative error 1.843249202981517e-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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations 10157 Total Elapsed Time 1 Minutes 59 Seconds Elapsed Time(since restart) 1 Minutes 59 Seconds Time to Timeout 1 Minutes 1.0 Seconds Percent Done 100.01723076921505%