Gibbs Phenomenon in Laplace's Equation for Heat Transfer

This Demonstration plots the solution to Laplace's equation for a square plate, .

The solution is given by

,

where and are the length and height of the plate (here ) and

,

where .

You can vary the temperature along the left edge. As you increase the number of terms , observe the Gibbs phenomena at the corners and along the edge where the temperature is higher.

[1] R. Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 4th ed., Saddle River, NJ: Prentice Hall, 2003.

[1] J. R. Brannan and W. E. Boyce, Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications, New York: John Wiley and Sons, 2010.