##############ECHO OF PROBLEM################# ##############temp/expt_c_linpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 , ( 0.2 * x + 0.3 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(1.0); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(7.2134752044448170367996234050095)*expt(c(2.0),(c(0.2)*c(x)+c(0.3)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 10.2013944659679 y[1] (numeric) = 10.2013944659679 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 1.1 y[1] (closed_form) = 10.34380062584569 y[1] (numeric) = 10.34380062584569 absolute error = 1.77635683940025e-15 relative error = 1.717315427524512e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 1.2 y[1] (closed_form) = 10.48819470163427 y[1] (numeric) = 10.48819470163427 absolute error = 1.77635683940025e-15 relative error = 1.693672638555669e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 1.3 y[1] (closed_form) = 10.63460444360563 y[1] (numeric) = 10.63460444360563 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 1.4 y[1] (closed_form) = 10.78305798941109 y[1] (numeric) = 10.78305798941109 absolute error = 1.77635683940025e-15 relative error = 1.647359071187991e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 1.5 y[1] (closed_form) = 10.93358386948899 y[1] (numeric) = 10.93358386948899 absolute error = 1.77635683940025e-15 relative error = 1.6246793920494e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 1.600000000000001 y[1] (closed_form) = 11.08621101254771 y[1] (numeric) = 11.08621101254771 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 1.700000000000001 y[1] (closed_form) = 11.24096875112537 y[1] (numeric) = 11.24096875112537 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 1.800000000000001 y[1] (closed_form) = 11.39788682722705 y[1] (numeric) = 11.39788682722705 absolute error = 1.77635683940025e-15 relative error = 1.558496646200174e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 1.900000000000001 y[1] (closed_form) = 11.55699539804077 y[1] (numeric) = 11.55699539804077 absolute error = 1.77635683940025e-15 relative error = 1.537040362325827e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.000000000000001 y[1] (closed_form) = 11.71832504173318 y[1] (numeric) = 11.71832504173318 absolute error = 1.77635683940025e-15 relative error = 1.515879473452054e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.100000000000001 y[1] (closed_form) = 11.88190676332625 y[1] (numeric) = 11.88190676332624 absolute error = 1.77635683940025e-15 relative error = 1.495009912788588e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.2 y[1] (closed_form) = 12.04777200065591 y[1] (numeric) = 12.04777200065591 absolute error = 1.77635683940025e-15 relative error = 1.47442766953387e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.3 y[1] (closed_form) = 12.21595263041394 y[1] (numeric) = 12.21595263041394 absolute error = 1.77635683940025e-15 relative error = 1.45412878810423e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.399999999999999 y[1] (closed_form) = 12.38648097427416 y[1] (numeric) = 12.38648097427416 absolute error = 1.77635683940025e-15 relative error = 1.434109367373686e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.499999999999999 y[1] (closed_form) = 12.55938980510412 y[1] (numeric) = 12.55938980510412 absolute error = 1.77635683940025e-15 relative error = 1.41436555992421e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.599999999999999 y[1] (closed_form) = 12.73471235326357 y[1] (numeric) = 12.73471235326357 absolute error = 1.77635683940025e-15 relative error = 1.394893571306318e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.699999999999998 y[1] (closed_form) = 12.91248231299078 y[1] (numeric) = 12.91248231299078 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.799999999999998 y[1] (closed_form) = 13.09273384887809 y[1] (numeric) = 13.09273384887809 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.899999999999998 y[1] (closed_form) = 13.27550160243773 y[1] (numeric) = 13.27550160243773 absolute error = 1.77635683940025e-15 relative error = 1.338071353231629e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 2.999999999999997 y[1] (closed_form) = 13.46082069875946 y[1] (numeric) = 13.46082069875946 absolute error = 1.77635683940025e-15 relative error = 1.319649729502718e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.099999999999997 y[1] (closed_form) = 13.648726753261 y[1] (numeric) = 13.648726753261 absolute error = 1.77635683940025e-15 relative error = 1.301481721711395e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.199999999999997 y[1] (closed_form) = 13.83925587853277 y[1] (numeric) = 13.83925587853278 absolute error = 3.552713678800501e-15 relative error = 2.567127676504206e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.299999999999996 y[1] (closed_form) = 14.03244469127819 y[1] (numeric) = 14.0324446912782 absolute error = 3.552713678800501e-15 relative error = 2.531785271178496e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.399999999999996 y[1] (closed_form) = 14.22833031935079 y[1] (numeric) = 14.2283303193508 absolute error = 3.552713678800501e-15 relative error = 2.496929435190821e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.499999999999996 y[1] (closed_form) = 14.42695040888963 y[1] (numeric) = 14.42695040888963 absolute error = 7.105427357601002e-15 relative error = 4.925106939594639e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.599999999999995 y[1] (closed_form) = 14.62834313155427 y[1] (numeric) = 14.62834313155428 absolute error = 7.105427357601002e-15 relative error = 4.857301536955433e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.699999999999995 y[1] (closed_form) = 14.83254719186081 y[1] (numeric) = 14.83254719186082 absolute error = 8.881784197001252e-15 relative error = 5.988037039164135e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.799999999999994 y[1] (closed_form) = 15.03960183462025 y[1] (numeric) = 15.03960183462026 absolute error = 8.881784197001252e-15 relative error = 5.905597963741251e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.899999999999994 y[1] (closed_form) = 15.24954685248072 y[1] (numeric) = 15.24954685248072 absolute error = 7.105427357601002e-15 relative error = 4.659435081144807e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 3.999999999999994 y[1] (closed_form) = 15.46242259357502 y[1] (numeric) = 15.46242259357503 absolute error = 1.06581410364015e-14 relative error = 6.892930892233018e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.099999999999993 y[1] (closed_form) = 15.67826996927492 y[1] (numeric) = 15.67826996927493 absolute error = 1.243449787580175e-14 relative error = 7.931039521688258e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.199999999999993 y[1] (closed_form) = 15.89713046205363 y[1] (numeric) = 15.89713046205365 absolute error = 1.243449787580175e-14 relative error = 7.821850556918328e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.299999999999993 y[1] (closed_form) = 16.11904613345813 y[1] (numeric) = 16.11904613345814 absolute error = 1.4210854715202e-14 relative error = 8.816188375877087e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.399999999999992 y[1] (closed_form) = 16.34405963219268 y[1] (numeric) = 16.3440596321927 absolute error = 1.77635683940025e-14 relative error = 1.086851663158022e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.499999999999992 y[1] (closed_form) = 16.57221420231531 y[1] (numeric) = 16.57221420231532 absolute error = 1.4210854715202e-14 relative error = 8.575109241115531e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.599999999999992 y[1] (closed_form) = 16.80355369154856 y[1] (numeric) = 16.80355369154858 absolute error = 1.4210854715202e-14 relative error = 8.457053178191366e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.699999999999991 y[1] (closed_form) = 17.0381225597064 y[1] (numeric) = 17.03812255970642 absolute error = 1.77635683940025e-14 relative error = 1.042577803496479e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.799999999999991 y[1] (closed_form) = 17.27596588723866 y[1] (numeric) = 17.27596588723868 absolute error = 1.77635683940025e-14 relative error = 1.028224326787078e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.899999999999991 y[1] (closed_form) = 17.5171293838948 y[1] (numeric) = 17.51712938389482 absolute error = 1.77635683940025e-14 relative error = 1.014068458633084e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 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] = 4.99999999999999 y[1] (closed_form) = 17.76165939750861 y[1] (numeric) = 17.76165939750863 absolute error = 2.131628207280301e-14 relative error = 1.200128974198942e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 180.3 Order of pole (ratio test) = 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt ( 2.0 , ( 0.2 * x + 0.3 ) ) ; Iterations = 81 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 102.5 %