**Project Topics**

Here are some sample topics for your term projects. It you would like
to work on one of these, please let me know. You are also encouraged to
choose your own topic, but would need to discuss it with me first.
It is advisable to make your selection fairly soon.

1. Solve the system of 1D Shallow Water equations in a periodic domain using
a spectral Fourier method.

2. Use the spectral Chebyshev method to solve the Kuramoto-Sivashinsky
equation in a bounded 1D domain with different sets of boundary conditions

3. Solve the Korteweg-de Vries (KdV) equation in a periodic 1D domain
using a spectral Galerkin method. Using analytical solutions available for
this problem perform careful error analysis.

4. Solve the Burgers equation in a 1D periodic domain using a wavelet method.

5. Solve the Kuramoto-Sivashinsky equation in 2D periodic domain using
a spectral Fourier method.

5. Use a spectral method to solve the Black-Scholes equation.

6. Use the complex step derivative method to compute the Jacobian of a quadratic
functional defined on solutions of the Burgers equation in 1D periodic domain.