MATLAB GUI: Heat Equation on the Whole Line

Description

This MATLAB GUI plots the solution to the one-dimensional heat equation, u_t = c²(u_xx + u_yy), 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

Download (right click on each link below) the following files into a directory. Set the MATLAB path to that directory and 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.

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© GUI developed by Joceline Lega, Spring 2007.