Program Listing for File RadauIA5.m

↰ Return to documentation for file (+Indigo/+Tableau/RadauIA5.m)

%
%> Class container for Radau IA method.
%
classdef RadauIA5 < Indigo.RungeKutta
  %
  methods
    %
    % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    %
    %> Radau IA method.
    %>
    %> \f[
    %> \begin{array}{c|ccc}
    %>   0 & \frac{1}{9} &
    %>   \frac{-1 - \sqrt{6}}{18} &
    %>   \frac{-1 + \sqrt{6}}{18} \\
    %>   \frac{3}{5} - \frac{\sqrt{6}}{10} & \frac{1}{9} &
    %>   \frac{11}{45} + \frac{7\sqrt{6}}{360} &
    %>   \frac{11}{45} - \frac{43\sqrt{6}}{360} \\
    %>   \frac{3}{5} + \frac{\sqrt{6}}{10} & \frac{1}{9} &
    %>   \frac{11}{45} + \frac{43\sqrt{6}}{360} &
    %>   \frac{11}{45} - \frac{7\sqrt{6}}{360} \\
    %>   \hline
    %>     & \frac{1}{9} &
    %>       \frac{4}{9} + \frac{\sqrt{6}}{36} &
    %>       \frac{4}{9} - \frac{\sqrt{6}}{36} \\
    %> \end{array}
    %> \f]
    %
    function this = RadauIA5()
      s6 = sqrt(6);
      tbl.A   = [1/9, -(s6+1)/18,       (s6-1)/18; ...
                 1/9, 11/45+7*s6/360,   11/45-43*s6/360; ...
                 1/9, 11/45+43*s6/360,  11/45-7*s6/360 ];
      tbl.b   = [1/9, 4/9+s6/36, 4/9-s6/36] ;
      tbl.b_e = []; % [-1, (s6/72)*(s6+6)^2, -(s6/72)*(s6-6)^2 ]; % ordine 2
      tbl.c   = [0,    3/5-sqrt(6)/10,     3/5+sqrt(6)/10]';
      this@Indigo.RungeKutta('RadauIA5', 5, tbl);
    end
    %
    % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    %
  end
  %
end