##############ECHO OF PROBLEM################# ##############temp/lin_sin_cospostode.ode################# diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* 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(glob__m1 * cos(c(2.0)*c(x) + c(3.0))/c(2.0) + sin(c(1.5)*c(x) -c(2.0))/c(1.5)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = -0.1417027474194901 y[1] (numeric) = -0.1417027474194901 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 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 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.2047060476124029 y[1] (closed_form) = -0.1795246312352974 y[1] (numeric) = -0.1795246312352975 absolute error = 8.326672684688674e-17 relative error = 4.638178408942204e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.007815149658914704 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1278 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3063029931782941 y[1] (closed_form) = -0.2208071996215787 y[1] (numeric) = -0.2208071996215788 absolute error = 5.551115123125783e-17 relative error = 2.514010019890353e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.007815149658914704 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2023 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000847890852708 y[1] (closed_form) = -0.2615200985868495 y[1] (numeric) = -0.2615200985868495 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.007815149658914704 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.242 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5016817346511622 y[1] (closed_form) = -0.3065768887655794 y[1] (numeric) = -0.3065768887655793 absolute error = 1.110223024625157e-16 relative error = 3.621352637165276e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.007815149658914704 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2468 Order of pole (three term test) = 22.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6032786802170536 y[1] (closed_form) = -0.3503763214851765 y[1] (numeric) = -0.3503763214851761 absolute error = 4.440892098500626e-16 relative error = 1.267463531689743e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.007815149658914704 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2114 Order of pole (three term test) = 22.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7048756257829449 y[1] (closed_form) = -0.3904069101168964 y[1] (numeric) = -0.3904069101168962 absolute error = 2.220446049250313e-16 relative error = 5.687517284428861e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.007815149658914704 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1416 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.8024407428948116 y[1] (closed_form) = -0.4228834499692268 y[1] (numeric) = -0.4228834499692266 absolute error = 2.775557561562891e-16 relative error = 6.563410229851436e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.005825460217189867 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05257 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.9010861617868738 y[1] (closed_form) = -0.447423776503849 y[1] (numeric) = -0.4474237765038487 absolute error = 2.775557561562891e-16 relative error = 6.203419905958025e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.002285267359089951 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] = 1.001637925586832 y[1] (closed_form) = -0.4615796231173156 y[1] (numeric) = -0.4615796231173157 absolute error = 5.551115123125783e-17 relative error = 1.202634354964778e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.002285267359089951 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] = 1.099904422027695 y[1] (closed_form) = -0.4628622118592585 y[1] (numeric) = -0.4628622118592584 absolute error = 1.110223024625157e-16 relative error = 2.398603723050824e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.002285267359089951 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2074 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200456185827649 y[1] (closed_form) = -0.4496979271205001 y[1] (numeric) = -0.4496979271204993 absolute error = 7.771561172376096e-16 relative error = 1.728173670298828e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.002285267359089951 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2455 Order of pole (three term test) = 22.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.301007949627602 y[1] (closed_form) = -0.4207311543794223 y[1] (numeric) = -0.4207311543794202 absolute error = 2.164934898019055e-15 relative error = 5.145649128865511e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.002285267359089951 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2444 Order of pole (three term test) = 22.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.401559713427555 y[1] (closed_form) = -0.3753749004560036 y[1] (numeric) = -0.3753749004559994 absolute error = 4.218847493575595e-15 relative error = 1.123902394233221e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.002285267359089951 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2044 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.499826209868419 y[1] (closed_form) = -0.3152689748531927 y[1] (numeric) = -0.3152689748531857 absolute error = 6.994405055138486e-15 relative error = 2.218551653677779e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.002285267359089951 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1336 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.600377973668372 y[1] (closed_form) = -0.2383419884805354 y[1] (numeric) = -0.238341988480525 absolute error = 1.040834085586084e-14 relative error = 4.366977435329593e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.002285267359089951 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04024 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.700449508203791 y[1] (closed_form) = -0.1476985787335563 y[1] (numeric) = -0.1476985787335416 absolute error = 1.471045507628332e-14 relative error = 9.959781063852031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.002210524207100102 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] = 1.799923097523291 y[1] (closed_form) = -0.04572061161928087 y[1] (numeric) = -0.04572061161926132 absolute error = 1.955380302121057e-14 relative error = 4.27680259048952e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.002210524207100102 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] = 1.901607211049891 y[1] (closed_form) = 0.06801052277300779 y[1] (numeric) = 0.06801052277303271 absolute error = 2.492450690283476e-14 relative error = 3.664801546375831e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.002210524207100102 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2159 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.00108080036939 y[1] (closed_form) = 0.1853237022934812 y[1] (numeric) = 0.1853237022935119 absolute error = 3.072542220650121e-14 relative error = 1.657932678133313e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.002210524207100102 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2478 Order of pole (three term test) = 22.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1005543896889 y[1] (closed_form) = 0.3050000752034605 y[1] (numeric) = 0.3050000752034849 absolute error = 2.442490654175344e-14 relative error = 8.008164104700628e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.002210524207100102 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2408 Order of pole (three term test) = 22.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.20002797900841 y[1] (closed_form) = 0.4231310889151805 y[1] (numeric) = 0.4231310889151986 absolute error = 1.809663530139005e-14 relative error = 4.276838969168168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.002210524207100102 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1963 Order of pole (three term test) = 22.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.30171209253502 y[1] (closed_form) = 0.5380407699553656 y[1] (numeric) = 0.5380407699553773 absolute error = 1.165734175856414e-14 relative error = 2.166627960095144e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.002210524207100102 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.119 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.40118568185453 y[1] (closed_form) = 0.6405530459582803 y[1] (numeric) = 0.6405530459582865 absolute error = 6.217248937900877e-15 relative error = 9.706064122448667e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.002210524207100102 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] = 2.500659271174039 y[1] (closed_form) = 0.7292750068716792 y[1] (numeric) = 0.7292750068716806 absolute error = 1.332267629550188e-15 relative error = 1.826838458738802e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.002210524207100102 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] = 2.600132860493549 y[1] (closed_form) = 0.8005261706155833 y[1] (numeric) = 0.8005261706155812 absolute error = 2.109423746787797e-15 relative error = 2.635046578384448e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.002210524207100102 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] = 2.701816974020159 y[1] (closed_form) = 0.8519303524887067 y[1] (numeric) = 0.8519303524887007 absolute error = 5.995204332975845e-15 relative error = 7.037200066252268e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.002210524207100102 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2233 Order of pole (three term test) = 22.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.801290563339669 y[1] (closed_form) = 0.8785437732429497 y[1] (numeric) = 0.8785437732429431 absolute error = 6.661338147750939e-15 relative error = 7.582249570971387e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.002210524207100102 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2495 Order of pole (three term test) = 22.53 NO COMPLEX POLE (six term test) for Equation 1 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 56.44 %