Program Listing for File LStableDirk4.m

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%
%> Class container for Merson's 4(5) method.
%
classdef LStableDirk4 < Indigo.RungeKutta
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  methods
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    % E. Hairer and G. Wanner. Vol. 2: Stiff and Differential-Algebraic Problems : Solving Ordinary Differential Equations. Volume 2. Springer, Berlin, 1999.[BibTeX]
    % L. M. Skvortsov. Diagonally implicit runge-kutta methods for stiff problems. Computational Mathematics and Mathematical Physics, 46(12):2110-2123, 2006.[BibTeX]    %>
    %
    %
    function this = LStableDirk4()
      %x       = 1-sqrt(2)/2;
      gamma   = (3+sqrt(3))/6;
      %tbl.A   = [1/4,  0,   0,   0,     0; ...
      %           -1/4, 1/4, 0,   0,     0; ...
      %           1/8,  1/8, 1/4, 0,     0; ...
      %           -3/2, 3/4, 3/2, 1/4,   0; ...
      %           0 ,   1/6  2/3, -1/12, 1/4 ];
      %tbl.b   = [0,   1/6  2/3, -1/12, 1/4];
      tbl.A   = [1/4,      0,         0,      0,       0; ...
                 1/2,      1/4,       0,      0,       0; ...
                 17/50,    -1/25,     1/4,    0,       0; ...
                 371/1360, -137/2720, 15/544, 1/4,     0; ...
                 25/24 ,   -49/48,    125/16, -85/12, 1/4 ];
      tbl.b   = [25/24 ,   -49/48,    125/16, -85/12, 1/4];
      tbl.b_e = [];
      tbl.c   = tbl.A*ones(5,1);
      this@Indigo.RungeKutta('LStableDirk4', 4, tbl);
    end
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  end
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end