##############ECHO OF PROBLEM################# ##############temp/mtest6_sm_hpostode.ode################# diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK ## problem from Boyce DePrima - ## _Elementary Differential Equations and Boundary Value Problems_ ## page 269 ## t_start=1.5 ## did poorly with t_start := 0.5; t_end=5.0 $array_x1_init[0 + 1] = exact_soln_x1(t_start) ## I think following line should be omitted ## diff(x1,1,exact_soln_x1p(t_start)); $array_x2_init[0 + 1] = exact_soln_x2(t_start) $array_x2_init[1 + 1] = exact_soln_x2p(t_start) $glob_look_poles=true $glob_max_iter=100 $glob_max_h=0.000001 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.001 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_x1 (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(2.0 * c1 + 6.0 * c3 * exp(-t)) end def exact_soln_x1p (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( - 6.0 * c3 * exp(-t)) end def exact_soln_x2 (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)) end def exact_soln_x2p (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 opt_iter 1 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 3.5 estimated_steps 3500000.0 step_error 2.8571428571428573e-17 est_needed_step_err 2.8571428571428573e-17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 value3 9.958907642447062e-187 value3 7.130137005118816e-178 max_value3 7.130137005118816e-178 value3 7.130137005118816e-178 best_h 1.0e-06 START of Soultion TOP MAIN SOLVE Loop t[1] 1.5 x1[1] (analytic) 2.0004016342882673 x1[1] (numeric) 2.0004016342882673 absolute error 0.0 relative error 0.0% Correct digits 16 h 1.0e-06 x2[1] (analytic) 1.0040840464326821 x2[1] (numeric) 1.0040840464326821 absolute error 0.0 relative error 0.0% Correct digits 16 h 1.0e-06 NO POLE for equation 1 Complex estimate of poles used for equation 2 Radius of convergence 47615.070719104755 Order of pole 119326027.30161881 TOP MAIN SOLVE Loop t[1] 1.5010009999999177 x1[1] (analytic) 2.0004012324534965 x1[1] (numeric) 2.00040123205106 absolute error 4.024367505905957e-10 relative error 2.0117801572087923e-08% Correct digits 9 h 1.0e-06 x2[1] (analytic) 1.0040920297648699 x2[1] (numeric) 1.0040920299663558 absolute error 2.014859390442325e-10 relative error 2.0066481265807363e-08% Correct digits 9 h 1.0e-06 NO POLE for equation 1 Complex estimate of poles used for equation 2 Radius of convergence 47638.64167435228 Order of pole 119444282.43068811 TOP MAIN SOLVE Loop t[1] 1.5020009999998354 x1[1] (analytic) 2.0004008314215924 x1[1] (numeric) 2.0004008298134495 absolute error 1.6081429521364043e-09 relative error 8.03910359802026e-08% Correct digits 9 h 1.0e-06 x2[1] (analytic) 1.0041000212972822 x2[1] (numeric) 1.0041000221035001 absolute error 8.062179812640125e-10 relative error 8.029259676963167e-08% Correct digits 9 h 1.0e-06 NO POLE for equation 1 Complex estimate of poles used for equation 2 Radius of convergence 47662.66759083668 Order of pole 119564738.38044918 TOP MAIN SOLVE Loop t[1] 1.5030009999997531 x1[1] (analytic) 2.0004004307905197 x1[1] (numeric) 2.0004004271733997 absolute error 3.6171199369050555e-09 relative error 1.8081979393873852e-07% Correct digits 8 h 1.0e-06 x2[1] (analytic) 1.004108029029369 x2[1] (numeric) 1.0041080308451762 absolute error 1.8158072823126759e-09 relative error 1.8083784113029593e-07% Correct digits 8 h 1.0e-06 NO POLE for equation 1 Complex estimate of poles used for equation 2 Radius of convergence 47686.40901948246 Order of pole 119683919.87087756 TOP MAIN SOLVE Loop t[1] 1.5040009999996709 x1[1] (analytic) 2.000400030559878 x1[1] (numeric) 2.000400024130508 absolute error 6.4293699253425984e-09 relative error 3.2140421051399037e-07% Correct digits 8 h 1.0e-06 x2[1] (analytic) 1.0041160529933622 x2[1] (numeric) 1.00411605622524 absolute error 3.2318778764306444e-09 relative error 3.218629825502859e-07% Correct digits 8 h 1.0e-06 NO POLE for equation 1 Complex estimate of poles used for equation 2 Radius of convergence 47710.403646833154 Order of pole 119804318.7533549 TOP MAIN SOLVE Loop t[1] 1.5050009999995886 x1[1] (analytic) 2.000399630729267 x1[1] (numeric) 2.000399620684373 absolute error 1.0044893805627453e-08 relative error 5.021443541241547e-07% Correct digits 8 h 1.0e-06 x2[1] (analytic) 1.0041240932215574 x2[1] (numeric) 1.0041240982775874 absolute error 5.056030039085613e-09 relative error 5.035264140375539e-07% Correct digits 8 h 1.0e-06 NO POLE for equation 1 Complex estimate of poles used for equation 2 Radius of convergence 47733.917333656755 Order of pole 119922568.47114874 TOP MAIN SOLVE Loop t[1] 1.5060009999995063 x1[1] (analytic) 2.000399231298286 x1[1] (numeric) 2.0003992168345843 absolute error 1.4463701791811445e-08 relative error 7.230407593400397e-07% Correct digits 8 h 1.0e-06 x2[1] (analytic) 1.0041321497463154 x2[1] (numeric) 1.0041321570362145 absolute error 7.289899128792854e-09 relative error 7.259900134294653e-07% Correct digits 8 h 1.0e-06 NO POLE for equation 1 Complex estimate of poles used for equation 2 Radius of convergence 47758.007568432964 Order of pole 120043564.1809912 TOP MAIN SOLVE Loop t[1] 1.507000999999424 x1[1] (analytic) 2.000398832266537 x1[1] (numeric) 2.000398812580749 absolute error 1.9685788110734848e-08 relative error 9.840931614837034e-07% Correct digits 8 h 1.0e-06 x2[1] (analytic) 1.0041402226000624 x2[1] (numeric) 1.004140232535169 absolute error 9.93510651525753e-09 relative error 9.894142562611566e-07% Correct digits 8 h 1.0e-06 NO POLE for equation 1 Complex estimate of poles used for equation 2 Radius of convergence 47782.06395563326 Order of pole 120164479.41014141 TOP MAIN SOLVE Loop t[1] 1.5080009999993418 x1[1] (analytic) 2.0003984336336202 x1[1] (numeric) 2.000398407922458 absolute error 2.5711162088271067e-08 relative error 1.2853020506303871e-06% Correct digits 7 h 1.0e-06 x2[1] (analytic) 1.0041483118152892 x2[1] (numeric) 1.0041483248085745 absolute error 1.2993285336548865e-08 relative error 1.2939607808591278e-06% Correct digits 7 h 1.0e-06 NO POLE for equation 1 Complex estimate of poles used for equation 2 Radius of convergence 47805.719811818635 Order of pole 120283560.08539896 Finished! Maximum Time Reached before Solution Completed! diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; Iterations 8129 Total Elapsed Time 3 Minutes 0.0 Seconds Elapsed Time(since restart) 3 Minutes 0.0 Seconds Expected Time Remaining 21 Hours 28 Minutes 30.77491412399104 Seconds Optimized Time Remaining 21 Hours 28 Minutes 30.77491412399104 Seconds Expected Total Time 21 Hours 31 Minutes 30.77491412399104 Seconds Time to Timeout 0.0 Seconds Percent Done 0.2322857142666049%