Program Listing for File Ralston4.m

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%
%> Class container for Ralston's method.
%
classdef Ralston4 < Indigo.RungeKutta
  %
  methods
    %
    % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    %
    %> Ralston's method.
    %>
    %> \f[
    %> \begin{array}{c|ccccc}
    %>   0           & 0   & 0 & 0 & 0 \\
    %>   \frac{2}{5} & 0.4 & 0 & 0 & 0 \\
    %>   \frac{7}{8}-\frac{3}{16}\sqrt{5} &
    %>   \frac{357}{256}\sqrt{5}-\frac{2889}{1024} &
    %>   \frac{3785}{1024}-\frac{405}{256}\sqrt{5} &
    %>    0 &
    %>    0 \\
    %>   1 &
    %>   \frac{1047}{3020}\sqrt{5}-\frac{673}{1208} &
    %>   -\frac{975}{2552}-\frac{1523}{1276}\sqrt{5} &
    %>   \frac{93408}{48169}+\frac{203968}{240845}\sqrt{5} &
    %>   0 \\
    %>   \hline
    %>     & \frac{263}{1812}+\frac{2}{151}\sqrt{5} &
    %>     \frac{125}{3828}-\frac{250}{957}\sqrt{5} &
    %>     \frac{3426304}{5924787}+\frac{553984}{1974929}\sqrt{5} &
    %>     \frac{10}{41}-\frac{4}{123}\sqrt{5}
    %> \end{array}
    %> \f]
    %
    function this = Ralston4()
      S5  = sqrt(5);
      A31 = (357/256)*S5-2889/1024;
      A32 = 3785/1024-(405/256)*S5;
      A41 = (1047/3020)*S5-673/1208;
      A42 = -975/2552-(1523/1276)*S5;
      A43 = 93408/48169+(203968/240845)*S5;
      B1  = 263/1812+(2/151)*S5;
      B2  = 125/3828-(250/957)*S5;
      B3  = 3426304/5924787+(553984/1974929)*S5;
      B4  = 10/41-(4/123)*S5;
      C2  = 2/5;
      C3  = 7/8-(3/16)*S5;
      tbl.A   = [0,   0,    0,   0; ...
                 0.4, 0,    0,   0; ...
                 A31, A32,  0,   0; ...
                 A41, A42,  A43, 0];
      tbl.b   = [B1, B2, B3, B4];
      tbl.b_e = [];
      tbl.c   = [0, C2, C3, 1]';
      this@Indigo.RungeKutta('Ralston4', 4, tbl);
    end
    %
    % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    %
  end
  %
end