Program Listing for File QinZhang.m

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%
%> Class container for Merson's 4(5) method.
%
classdef QinZhang < Indigo.RungeKutta
  %
  methods
    %
    % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    %
    %> Qin and Zhang's two-stage, 2nd order, symplectic Diagonally Implicit Runge-Kutta method:.
    %>
    %> \f[
    %> \begin{array}{c|cc}
    %>   1/4 & 1/4 &     \\
    %>   3/4 & 1/2 & 1/4 \\
    %>   \hline
    %>      &  1/2 & 1/2 \\
    %> \end{array}
    %> \f]
    %
    %
    function this = QinZhang()
      gamma = 1-1/sqrt(2);
      %tbl.A   = [1/2,  0,   0; ...
      %           -1/2, 1/2, 0; ...
      %           0,    1/2, 1/2];
      %tbl.b   = [0,    1/2, 1/2];
      lambda = 0.4358665215084589994160194511935568425292;
      b1     = (lambda*(16-6*lambda)-1)/4;
      b2     = (5+lambda*(6*lambda-20))/4;
      tbl.A   = [lambda,       0,      0; ...
                 (1-lambda)/2, lambda, 0; ...
                 b1,           b2,     lambda];
      tbl.b   = [b1, b2, lambda];
      tbl.b_e = [];
      tbl.c   = tbl.A*ones(3,1);
      this@Indigo.RungeKutta('QinZhang', 3, tbl);
    end
    %
    % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    %
  end
  %
end