Matrices: Matrix norm. Spectral decomposition, Singular value decomposition, convergence and perturbation theorem, Matrix eigenvalue problem, Eigen-value by iteration, Q-R Factorization, Generalized inverse of matrices; Approximation of functions: General function spaces, Least square approximation, orthogonal polynomials, approximation with rational functions, Pade’s approximation; Differential equations: Nonlinear system of differential equations- method of successive approximations, Use of Pade’s approximation, Lyapunov and Riccati equations.
Boundary Value Problems: Method of undetermined coefficients, Difference scheme based on quadrature formulas, solution of tridiagonal system, moving boundary conditions, boundary conditions at infinity, Non-linear boundary value problems, convergence of difference schemes, linear eigenvalue problems; Partial Differential Equations: Parabolic, Elliptic and Hyperbolic differential equations.
Suggested Text:
- Gene H. Golub and James M. Ortega. Scientific Computing and Differential Equations, Academic Press NewYork.
- K. Jain. Numerical Solution of Differential Equations
- G. Ancona. Computational Methods for Applied Science and Engineering
- Kendall E. Atkinson. An Introduction to Numerical Analysis
- Evans, Lawrence C. Partial Differential Equations.