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Highlights from
Chebfun V4

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Chebfun V4



30 Apr 2009 (Updated )

Numerical computation with functions instead of numbers.

Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

classdef chebgui
% Chebgui is a graphical user interface to Chebfun's capabilities for
% solving ODEs and PDEs (ordinary and partial differential equations) and
% eigenvalue problems. More precisely, it deals with the following classes
% of problems.  In all cases both single equations and systems of equations
% can be treated, as well as integral and integro-differential equations.
% ODE BVP (boundary-value problem): an ODE or system of ODEs on an interval
% [a,b] with boundary conditions at both boundaries.
% ODE IVP (initial-value problem): an ODE or system of ODEs on an interval
% [a,b] with boundary conditions at just one boundary. (However, for
% complicated IVPs like the Lorenz equations, other methods such as
% chebfun/ode45 will be much more effective.)
% ODE EIGENVALUE PROBLEM: a differential or integral operator or system of
% operators on an interval [a,b] with homogeneous boundary conditions,
% where we want to compute one or more eigenvalues and eigenfunctions.
% Generalized eigenvalue problems L*u = lambda*M*u are also treated.
% PDE BVP: a time-dependent problem of the form u_t = N(u,x,t), where N is
% a linear or nonlinear differential operator.
% For ODEs, Chebgui assumes that the independent variable, which varies
% over the interval [a,b], is either x or t, and that the dependent
% variable(s) have name(s) different from x and t.
% For eigenvalue problems, Chebgui assumes that the eigenvalue is called
% lambda or lam or l.
% For PDEs, Chebgui assumes that the space variable on [a,b] is x and that
% the time variable, which ranges over a span t1:dt:t2 is t.
% Here is a three-sentence sketch of how the solutions are computed.  The
% ODE and eigenvalue problems are solved by Chebfun's automated Chebyshev
% spectral methods underlying the Chebfun commands <backslash> and
% SOLVEBVP.  The discretizations involved will be described in a
% forthcoming paper by Driscoll and Hale, and the Newton and damped Newton
% iterations used to handle nonlinearity will be described in a forthcoming
% paper by Birkisson and Driscoll.  The PDE problems are solved by
% Chebfun's PDE15S method, due to Hale, which is based on spectral
% discretization in x coupled with Matlab's ODE15S solution in t.
% To use Chebgui, the simplest method is to type chebgui at the Matlab
% prompt.  The GUI will appear with a demo already loaded and ready to run;
% you can get its solution by pressing the green SOLVE button.  To try
% other preloaded examples, open the DEMOS menu at the top.  To input your
% own example on the screen, change the windows in ways which we hope are
% obvious. Inputs are vectorized, so x*u and x.*u are equivalent, for
% example.  Derivatives are indicated by single or double primes, so a
% second derivative is u'' or u".
% The GUI allows various types of syntax for describing the differential
% equation and boundary conditions of problems. The differential equations
% can either be in anonymous function form, e.g.
%   @(u) diff(u,2)+x.*sin(u)
% or a "natural syntax form", e.g.
%   u''+x.*sin(u)
% The first format gives extra flexibility, e.g. for specifying an
% integral operator with the help of CUMSUM.
% Boundary conditions can be in either of these two forms, or alternatively
% one can specify homogeneous Dirichlet or Neumann conditions simply by
% typing 'dirichlet' or 'neumann' in the relevant fields.  Eigenvalue
% problems can be specified by equations like
%   -u" + x^2*u = lambda*u
% The GUI supports systems of coupled equations, where the problem can most
% easily be set up with a format like
%   u' + sin(v) = u+v
%   cos(u) + v' = 0
% or
%   u" = lambda*v
%   v" = lambda*(u+u')
% Finally, the most valuable Chebgui capability of all is the "Export to
% m-file" button.  With this feature, you can turn an ODE or PDE solution
% from the GUI into an M-file in standard Chebfun syntax.  This is a great
% starting point for more serious explorations.
% CHEBGUI is also the constructor for chebgui objects. For example
%    chebg = chebgui('type','bvp','domain','[-1,1]', ...
%                    'de','u" = sin(u)','lbc','u = 1','rbc','u = 0')
%    show(chebg)
% See also chebop/solvebvp, chebop/eigs, chebfun/pde15s, chebfun/ode45,
% chebfun/ode113, chebfun/ode15s, chebfun/bvp4c, chebfun/bvp5c.

% Copyright 2011 by The University of Oxford and The Chebfun Developers.
% See for Chebfun information.
        type = '';          % Type of chebgui (bvp, pde, or eig)
        domain = '';        % Spacial domain (may contain breakpoints)
        DE = '';            % Differential equation, or rhs in u_t = ... for PDEs
        LBC = '';           % Left BCs
        RBC = '';           % Right BCs
        BC = '';            % Interior / nonstandard BCs
        timedomain = '';    % Time domain (should include breakpoints)
        sigma = '';         % Third input to an EIGS call
        init = '';          % Initial guess/condition for nonlin BVPs/PDEs
        tol = 1e-10;        % Solution tolerance
        options = struct('damping','1','plotting','0.5','grid',1,...
            'pdeholdplot',0,'fixYaxisLower','', ...
        function c = chebgui(varargin)
            % No input --> load random example to the GUI window
            if isempty(varargin)
                c = loadexample(chebgui('type','bvp'),-1);
                show(c); % Open the GUI
            v1 = varargin{1};
            % Single input --> load existing chebgui object/file
            if nargin == 1
                if isa(v1,'chebgui')
                    % Calling the chebgui constructor with a chebgui loads the GUI`
                    c = v1;
                elseif ischar(v1)
                    % Calling with a single string loads a .guifile`
                    if ~exist(v1,'file')
                        % Throw a method if this .guifie is not found
                            'Unable to find file: %s',v1);
                    % Load the existing demp
                    c = loaddemos(chebgui('type','bvp'),v1);
                if nargout == 0
                    show(c); % Open the GUI
            % Multiple inputs --> loop through them (using CHEBGUI/SET)
            k = 1;
            while k < nargin
                c = set(c,varargin{k:k+1});
                k = k + 2;


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