Program Listing for File RadauIIA5.m

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%
%> Class container for Radau IIA5 method.
%
classdef RadauIIA5 < Indigo.RungeKutta
  %
  methods
    %
    % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    %
    %> Radau IIA5 method.
    %>
    % https://www.math.auckland.ac.nz/~butcher/ODE-book-2008/Tutorials/IRK.pdf
    %>
    %> \f[
    %> \begin{array}{c|ccc}
    %>   \frac{2}{5} - \frac{\sqrt{6}}{10} &
    %>   \frac{11}{45} - \frac{7 \sqrt{6}}{360} &
    %>   \frac{37}{225} - \frac{169 \sqrt{6}}{1800}  &
    %>   -\frac{2}{225} + \frac{\sqrt{6}}{75}  \\
    %>   \frac{2}{5} + \frac{\sqrt{6}}{10} &
    %>   \frac{37}{225} + \frac{169 \sqrt{6}}{1800} &
    %>   \frac{11}{45} + \frac{7 \sqrt{6}}{360} &
    %>   -\frac{2}{225} - \frac{\sqrt{6}}{75} \\
    %>   1 &
    %>   \frac{4}{9} - \frac{\sqrt{6}}{36} &
    %>   \frac{4}{9} + \frac{\sqrt{6}}{36} &
    %>   \frac{1}{9} \\
    %>   \hline
    %>     & \frac{4}{9} - \frac{\sqrt{6}}{36} &
    %>       \frac{4}{9} + \frac{\sqrt{6}}{36} &
    %>       \frac{1}{9} \\
    %> \end{array}
    %> \f]
    %
    function this = RadauIIA5()
      s6 = sqrt(6);
      tbl.A   = [11/45-7*s6/360,     37/225-169*s6/1800, -2/225+s6/75; ...
                 37/225+169*s6/1800, 11/45+7*s6/360,     -2/225-s6/75; ...
                 4/9-s6/36,          4/9+s6/36,          1/9];
      tbl.b   = [4/9-s6/36, 4/9+s6/36, 1/9];
      tbl.b_e = [];
      tbl.c   = [2/5-sqrt(6)/10, 2/5+sqrt(6)/10, 1]';
      this@Indigo.RungeKutta('RadauIIA5', 5, tbl);
    end
    %
    % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    %
  end
  %
end