MATH6190 Numerical Analysis

 

Number of Credits : 4

 

PRE-REQUISITE: NONE

 

Course Description:

Review of Computer errors. Programming in MATLAB. Solution of non-linear equations.

Numerical linear Algebra

LU and Cholesky factorisations factorizations. Pivoting.  Norms and analysis of errors. Iterative methods. The matrix eigenvalue problem. The singular-value decomposition and  pseudo-inverses.

Approximation of functions

Polynomial interpolation. Hermite interpolation. Spline interpolation. Best approximation: Least squares and Chebyshev.

Trigonometric interpolation and the Fast Fourier Transform.

Numerical differentiation and integration

Gaussian and adaptive quadrature.

Numerical solution of ordinary differential equations

Existence and uniqueness of solutions. Runge-Kutta and multi-step methods. Local and global errors. Stability.

Boundary-value problems: Shooting methods. Finite-difference methods. Collocation. 

Stiff equations.

Introduction to the numerical solution of partial differential equation

Elliptic, parabolic and hyperbolic partial differential equations.

 

Assessment:

Coursework                                                         25%

Final Examination One 3 hour written paper           75%