Program Listing for File LobattoIIIA6.m

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%
%> Class container for Lobatto IIIA6 method.
%
classdef LobattoIIIA6 < Indigo.RungeKutta
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  methods
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    %
    %> Lobatto IIIA6 method.
    %>
    % http://www.jaac-online.com/data/article/jaac/preview/pdf/20170325.pdf
    % Symplectic Runge-Kutta Methods of High Order Based on W-Transformation,
    % Kaifeng Xia, Yuhao Cong1 and Geng Sun. Journal of Applied Analysis and
    % Computation, Volume 7, Number 3, August 2017, 1185-1199
    %
    function this = LobattoIIIA6()
      s5      = sqrt(5);
      tbl.A   = [0,           0,              0,              0; ...
                 (11+s5)/120, (25-s5)/120,    (25-13*s5)/120, (-1+s5)/120; ...
                 (11-s5)/120, (25+13*s5)/120, (25+s5)/120,    (-1-s5)/120; ...
                 1/12,        5/12,           5/12,           1/12];
      tbl.b   = [1/12,        5/12,           5/12,           1/12];
      tbl.b_e = [];
      tbl.c   = tbl.A*ones(4,1);
      this@Indigo.RungeKutta('LobattoIIIA6', 6, tbl);
    end
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  end
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end