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.
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