Heat Equation on the Whole Line

Description

This MATLAB GUI plots the solution to the one-dimensional heat equation, u_t = c²u_xx, as a function of time and for "top hat" initial conditions.

The solution is calculated as the convolution of the heat kernel with the initial condition. The resulting integral is re-written in terms of the error function and is evaluated numerically. Changing the diffusion coefficient (c²) amounts to rescaling the time variable.

How to use the GUI

Use the sliders in the Initial conditions panel to choose the height and the width of the "top hat" initial condition.

Adjust the diffusion coefficient.

Use the slider under the plot window to see how the solution evolves in time. The solution at time t is shown in red and the initial condition in blue.

Download

To download the GUI, right click on each of the links below, and save the corresponding files into a directory. Set the MATLAB path to that directory and then type Heat_Equation_WL at the MATLAB prompt.

• Heat_Equation_WL.m
• Heat_Equation_WL.fig

Type help Heat_Equation_WL at the MATLAB prompt if you need to be reminded of how to use the GUI.

GUI developed by Joceline Lega, Spring 2007.