715 - Methods of Computational Math II

Math/CS 715 can be taken either as a continuation of Math/CS 714 (Computational Math I: Finite Difference Methods) or a stand-alone course for students with prior knowledge of finite difference methods. This course will focus on alternatives to the finite difference method including spectral methods (useful for problems with relatively simple geometry where high-order accuracy is required), finite element methods (useful for problems with complicated geometry), and mesh-free methods (alternative to previously mentioned methods that avoids a numerical grid). The approach in Math/CS 715 will be to present the basic theory of these methods and then discuss practical implementation issues related to improving accuracy and efficiency. HW assignments will involve both pencil & paper analysis and computer programming. The final exam in the course will be a presentation of a topic chosen by the student related to the material covered in the course.

Topics:

* Spectral Methods (Sources: J.P. Boyd, Chebyshev and Fourier Spectral Methods. L.N. Trefethen, Spectral Methods in MATLAB.)
* Finite Element Methods (Source: C. Grossmann, H-G. Roos, and M. Stynes. Numerical Treatment of Partial Differential Equations.)
* Mesh-Free Methods (Source: various journal articles.)