Finite difference, finite element, and spectral methods for elliptic, parabolic and hyperbolic partial differential equations; discussion of discretization schemes, truncation error, consistency, stability, accuracy and convergence; explicit vs. implicit schemes; implementation of Dirichlet, Neumann and Robin boundary conditions; operator splitting; Godunov methods for hyperbolic systems; direct and iterative methods for elliptic systems; Gauss-Seidel, SOR and multigrid methods; Fourier and Chebyshev based spectral and pseudo-spectral methods. Prerequisites: partial differential equations and numerical analysis.
2013 Claremont Graduate University 
150 E. 10th St., Claremont, CA 91711 