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