3.0

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We discuss numerical methods for solving partial differential equations, explaining how solution methods must be appropriate to the mathematical structure of the equation. Specific topics will be Hyperbolic PDE’s (CFL stability condition, characteristics, convergence, nonlinear conservation laws, shock capturing), Parabolic PDE’s (boundary conditions, explicit and implicit discretizations, consistency, stability, and convergence, operator splitting), Elliptic PDE’s (iterative methods, variational formulations). We shall focus mainly on finite-difference schemes, but other methods such as finite element, finite volume, spectral methods, Chebyshev polynomials, etc. may be discussed as time permits. All numerical methods will be illustrated with Matlab scripts. Prior knowledge of Numerical Linear Algebra is strongly recommended. A good introductory course in the mathematics of Partial Differential Equations would also be helpful, but this material will be reviewed as necessary.