### MA6270 Numerical Solution of PDE

#### Course Details

Parabolic Equations: explicit and implicit finite difference approximations to one dimensional heat equation, Alternating Direction Implicit (ADI) method, Hyperbolic Equations: Characteristic method, finite difference solution of second order wave equation, Convergence, consistency and stability analysis, Elliptic equations: finite difference method in polar coordinates, techniques near curved boundaries, improvement of accuracy, methods to accelerate the convergence, Finite element method: types of integral formulations, one and two dimensional elements, Galerkin formulation, application to Dirichlet and Neumann problems.

#### Course References:

**TextBooks:**

1. G D Smith, Numerical solution of partial differential equations: Finite difference methods, Oxford University press, 1977.

2. G. Evans, J. Blackledge, P. Yardley, Numerical Methods for Partial Differential Equations, 2nd edition, Springer, 2001.

**Reference Books:**

1 S. Larsson, V. Thomee, Partial Differential Equations with Numerical Methods, Springer, 2003.

2. K. Eriksson, D. Estep, P. Hansbo, C. Johnson, Computational Differential Equations, Cambridge Univ. Press, 1996.

3. H. P. Langtangen, Computational Partial Differential Equations, Numerical Methods and Diffpack Programming, 2nd edition, Springer, 2003.

4. D. Braess Finite Elements, 2nd edition, Cambridge Univ. Press, 2001.

5. C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge Univ. Press, 1987.