/usr/share/octave/packages/odepkg-0.8.5/odepkg_examples_ode.m is in octave-odepkg 0.8.5-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 | %# Copyright (C) 2008-2012, Thomas Treichl <treichl@users.sourceforge.net>
%# OdePkg - A package for solving ordinary differential equations and more
%#
%# This program is free software; you can redistribute it and/or modify
%# it under the terms of the GNU General Public License as published by
%# the Free Software Foundation; either version 2 of the License, or
%# (at your option) any later version.
%#
%# This program is distributed in the hope that it will be useful,
%# but WITHOUT ANY WARRANTY; without even the implied warranty of
%# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%# GNU General Public License for more details.
%#
%# You should have received a copy of the GNU General Public License
%# along with this program; If not, see <http://www.gnu.org/licenses/>.
%# -*- texinfo -*-
%# @deftypefn {Function File} {[@var{}] =} odepkg_examples_ode (@var{})
%# Open the ODE examples menu and allow the user to select a demo that will be evaluated.
%# @end deftypefn
function [] = odepkg_examples_ode ()
vode = 1; while (vode > 0)
clc;
fprintf (1, ...
['ODE examples menu:\n', ...
'==================\n', ...
'\n', ...
' (1) Solve a non-stiff "Van der Pol" example with solver "ode78"\n', ...
' (2) Solve a "Van der Pol" example backward with solver "ode23"\n', ...
' (3) Solve a "Pendulous" example with solver "ode45"\n', ...
' (4) Solve the "Lorenz attractor" with solver "ode54"\n', ...
' (5) Solve the "Roessler equation" with solver "ode78"\n', ...
'\n', ...
' Note: There are further ODE examples available with the OdePkg\n', ...
' testsuite functions.\n', ...
'\n', ...
' If you have another interesting ODE example that you would like\n', ...
' to share then please modify this file, create a patch and send\n', ...
' your patch with your added example to the OdePkg developer team.\n', ...
'\n' ]);
vode = input ('Please choose a number from above or press <Enter> to return: ');
clc; if (vode > 0 && vode < 6)
%# We can't use the function 'demo' directly here because it does
%# not allow to run other functions within a demo.
vexa = example (mfilename (), vode);
disp (vexa); eval (vexa);
input ('Press <Enter> to continue: ');
end %# if (vode > 0)
end %# while (vode > 0)
%!demo
%! # In this example the non-stiff "Van der Pol" equation (mu = 1) is
%! # solved and the results are displayed in a figure while solving.
%! # Read about the Van der Pol oscillator at
%! # http://en.wikipedia.org/wiki/Van_der_Pol_oscillator.
%!
%! function [vyd] = fvanderpol (vt, vy, varargin)
%! mu = varargin{1};
%! vyd = [vy(2); mu * (1 - vy(1)^2) * vy(2) - vy(1)];
%! endfunction
%!
%! vopt = odeset ('RelTol', 1e-8);
%! ode78 (@fvanderpol, [0 20], [2 0], vopt, 1);
%!demo
%! # In this example the non-stiff "Van der Pol" equation (mu = 1) is
%! # solved in forward and backward direction and the results are
%! # displayed in a figure after solving. Read about the Van der Pol
%! # oscillator at http://en.wikipedia.org/wiki/Van_der_Pol_oscillator.
%!
%! function [ydot] = fpol (vt, vy, varargin)
%! ydot = [vy(2); (1 - vy(1)^2) * vy(2) - vy(1)];
%! endfunction
%!
%! vopt = odeset ('NormControl', 'on');
%! vsol = ode23 (@fpol, [0, 20], [2, 0], vopt);
%! subplot (2, 3, 1); plot (vsol.x, vsol.y);
%! vsol = ode23 (@fpol, [0:0.1:20], [2, 0], vopt);
%! subplot (2, 3, 2); plot (vsol.x, vsol.y);
%! vsol = ode23 (@fpol, [-20, 20], [-1.1222e-3, -0.2305e-3], vopt);
%! subplot (2, 3, 3); plot (vsol.x, vsol.y);
%!
%! vopt = odeset ('NormControl', 'on');
%! vsol = ode23 (@fpol, [0:-0.1:-20], [2, 0], vopt);
%! subplot (2, 3, 4); plot (vsol.x, vsol.y);
%! vsol = ode23 (@fpol, [0, -20], [2, 0], vopt);
%! subplot (2, 3, 5); plot (vsol.x, vsol.y);
%! vsol = ode23 (@fpol, [20:-0.1:-20], [-2.0080, 0.0462], vopt);
%! subplot (2, 3, 6); plot (vsol.x, vsol.y);
%!demo
%! # In this example a simple "pendulum with damping" is solved and the
%! # results are displayed in a figure while solving. Read about the
%! # pendulum with damping at
%! # http://en.wikipedia.org/wiki/Pendulum
%!
%! function [vyd] = fpendulum (vt, vy)
%! m = 1; %# The pendulum mass in kg
%! g = 9.81; %# The gravity in m/s^2
%! l = 1; %# The pendulum length in m
%! b = 0.7; %# The damping factor in kgm^2/s
%! vyd = [vy(2,1); ...
%! 1 / (1/3 * m * l^2) * (-b * vy(2,1) - m * g * l/2 * sin (vy(1,1)))];
%! endfunction
%!
%! vopt = odeset ('RelTol', 1e-3, 'OutputFcn', @odeplot);
%! ode45 (@fpendulum, [0 5], [30*pi/180, 0], vopt);
%!demo
%! # In this example the "Lorenz attractor" implementation is solved
%! # and the results are plot in a figure after solving. Read about
%! # the Lorenz attractor at
%! # http://en.wikipedia.org/wiki/Lorenz_equation
%! #
%! # The upper left subfigure shows the three results of the integration
%! # over time. The upper right subfigure shows the force f in a two
%! # dimensional (x,y) plane as well as the lower left subfigure shows
%! # the force in the (y,z) plane. The three dimensional force is plot
%! # in the lower right subfigure.
%!
%! function [vyd] = florenz (vt, vy)
%! vyd = [10 * (vy(2) - vy(1));
%! vy(1) * (28 - vy(3));
%! vy(1) * vy(2) - 8/3 * vy(3)];
%! endfunction
%!
%! A = odeset ('InitialStep', 1e-3, 'MaxStep', 1e-1);
%! [t, y] = ode54 (@florenz, [0 25], [3 15 1], A);
%!
%! subplot (2, 2, 1); grid ('on');
%! plot (t, y(:,1), '-b', t, y(:,2), '-g', t, y(:,3), '-r');
%! legend ('f_x(t)', 'f_y(t)', 'f_z(t)');
%! subplot (2, 2, 2); grid ('on');
%! plot (y(:,1), y(:,2), '-b');
%! legend ('f_{xyz}(x, y)');
%! subplot (2, 2, 3); grid ('on');
%! plot (y(:,2), y(:,3), '-b');
%! legend ('f_{xyz}(y, z)');
%! subplot (2, 2, 4); grid ('on');
%! plot3 (y(:,1), y(:,2), y(:,3), '-b');
%! legend ('f_{xyz}(x, y, z)');
%!demo
%! # In this example the "Roessler attractor" implementation is solved
%! # and the results are plot in a figure after solving. Read about
%! # the Roessler attractor at
%! # http://en.wikipedia.org/wiki/R%C3%B6ssler_attractor
%! #
%! # The upper left subfigure shows the three results of the integration
%! # over time. The upper right subfigure shows the force f in a two
%! # dimensional (x,y) plane as well as the lower left subfigure shows
%! # the force in the (y,z) plane. The three dimensional force is plot
%! # in the lower right subfigure.
%!
%! function [vyd] = froessler (vt, vx)
%! vyd = [- ( vx(2) + vx(3) );
%! vx(1) + 0.2 * vx(2);
%! 0.2 + vx(1) * vx(3) - 5.7 * vx(3)];
%! endfunction
%!
%! A = odeset ('MaxStep', 1e-1);
%! [t, y] = ode78 (@froessler, [0 70], [0.1 0.3 0.1], A);
%!
%! subplot (2, 2, 1); grid ('on');
%! plot (t, y(:,1), '-b;f_x(t);', t, y(:,2), '-g;f_y(t);', \
%! t, y(:,3), '-r;f_z(t);');
%! subplot (2, 2, 2); grid ('on');
%! plot (y(:,1), y(:,2), '-b;f_{xyz}(x, y);');
%! subplot (2, 2, 3); grid ('on');
%! plot (y(:,2), y(:,3), '-b;f_{xyz}(y, z);');
%! subplot (2, 2, 4); grid ('on');
%! plot3 (y(:,1), y(:,2), y(:,3), '-b;f_{xyz}(x, y, z);');
%# Local Variables: ***
%# mode: octave ***
%# End: ***
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