--- /dev/null
+%# 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: ***
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff