MA 253: Numerical Methods for Partial Differential Equations
Finite difference methods for two point boundary value problems, Laplace
equation on the square, heat equation and symmetric hyperbolic systems in 1 D.
Lax equivalence theorem for abstract initial value problems. Introduction to
variational formulation and the Lax-Milgram lemma. Finite element methods for
elliptic and parabolic equations.
Suggested books and references:
Smith, G. D., Numerical solution of partial differential equations: Finite Difference Methods, Calarendon Press, 1985.
Evans, G. Blackledge, J. and Yardley, P., Numerical methods of partial differential equations, Springer-Verlag, 1999.