The University of Alabama 3 credits MATH
Finite difference methods for hyperbolic, parabolic, and elliptical partial differential equations; consistency, convergence, and order of accuracy of finite difference schemes; stability analysis and the Courant-Friedrichs-Lewy (CFL) condition; numerical dispersion and dissipation; finite difference schemes in higher dimensions; implicit methods and alternating direction implicit (ADI) schemes; a brief introduction to additional topics, such as spectral methods, pseudo-spectral methods, finite volume methods, and finite element methods, may be offered at the discretion of instructor. Students need to have experience in programming in a high-level programming language such as Python, MATLAB, C++, or FORTRAN.
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