Numerical Analysis Ii
Course Content and Outline
Basic definition of approximation, the Weierstrass theorem, the Korovkin
Theorem, best approximations, Chebyshev polynomials, trigonometric
approximations, splines and dual functional.
Numerical Solution of
ODEs. Ordinary differential equations: Euler's method and beyond. Multistep
methods. Runge–Kutta methods. Stiff equations. Geometric numerical integration.
systems. The Poisson equation. Finite difference schemes. The finite element
method. Spectral methods. Gaussian elimination for sparse linear equations.
methods for sparse linear equations. Multigrid
techniques. Conjugate gradients. Fast
Poisson solvers. Boundary-Value Problems. The Shooting Method. Finite
Differences. Boundary Derivative Conditions. Characteristic-Value Problems.
Introduction to numerical methods for partial differential equations.
equation. Hyperbolic equations. Application with MATLAB.
MODE OF DELIVERY
Lecture and discussion
- Reading and problem assignments
- Whiteboard and Markers
- Flip Charts
- LCD Projectors
- CDs, DVDs and Tapes