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.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


[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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.