MATH 322 - MATLAB GUIs
One-dimensional Heat Equation
© GUI developed by Zhiying
Sun, Spring 2007
Description
This MATLAB GUI illustrates the use of Fourier
series to simulate the diffusion of heat in a
domain of finite size. The quantity u
evolves according to the heat equation,
ut - uxx = 0,
and may satisfy Dirichlet, Neumann, or mixed
boundary conditions.
- The relevant Fourier basis depends on the
selected boundary conditions.
- The initial condition is expanded onto the
Fourier basis associated with the boundary
conditions. Only the first 4 modes are
shown.
- Each Fourier mode evolves in time
independently from the others. The corresponding
Fourier series is the solution to the heat
equation with the given boundary and intitial
conditions.
How to use the GUI
- Choose one type of boundary conditions. An
initial condition that satisfies the selected
boundary conditions is shown in blue in the top
right plot window.
- Click on button #1 to identify the Fourier
basis associated with the selected boundary
conditions. The first 4 modes are listed and
plotted in blue, as functions of x.
- Click on button #2 to compute the
coefficients of the first 4 modes in the Fourier
series expansion of the initial condition. Each
of these modes is plotted in red as a function of
x. Their superposition is shown in red in
the top right plot window, and can be compared to
the initial condition.
- Move the slider to see how each of the 4
modes evolves in time. The corresponding
truncated Fourier series is shown in red in the
top plot window.
Download
Download (right click
on each link below) the following files into a
directory. Set the MATLAB path to that directory
and type
Heat_Equation at the MATLAB
prompt.
Type
help Heat_Equation at the MATLAB
prompt if you need to be reminded of how to use the
GUI.
