APPLIED NUMERICAL ANALYSIS

Optional course 4 credits.

Lectures : 3 credits  Computer practices : 1 credit

I. Overview

We will cover the various topics for the numerical eigenvalue problems for linear systems, numerical solution to ordinary differential equations and numerical solutions of partial differential equations.

II. Prerequisites : Matlab .

III. Contents

          We cover chapters 5, 8, 9 of the book [1]

Chapter 1: Eigenvalue problems

1.1.1 Power method
1.1.2 Schur's and Gershgorin's theorems
1.1.3 Orthogonal factorizations
1.1.4 Least square problems
1.1.5 Singular value decomposition
1.1.6 QR algorithm (excluding convergence theory)

Chapter 2: Numerical solution of ordinary differential equations

2.1 Existence and uniqueness

2.2 Taylor series methods

2.3 Runge-Kutta methods

2.4 Multistep methods

2.5 Boundary value problems

2.6 Stiff equations

Chapter 3: Numerical solution of partial differential equations

3.1 Explicit and implicit methods for parabolic problems

3.2 Finite difference methods

3.3 Galerkin and Ritz methods

3.4 Multigrid methods

References

[1]. D. Kincaid and W. Cheney . Numerical Analysis: Mathematics of Scientific Computing, second edition', by . Brooks/Cole Publishing Co. 1996.
[2]. J. Douglas Faires, Richard L. Burden. Numerical Analysis , seven edition  (2004)