Module Identifier MAM4420
Module Title BOUNDARY VALUE PROBLEMS
Co-ordinator Professor Russell Davies
Semester Intended for use in future years
Next year offered N/A
Next semester offered N/A
Other staff Professor Tim Phillips
Pre-Requisite MA34410 , MA30210 , MA34110
Course delivery Lecture   20 x 1hour lectures
Seminars / Tutorials   7 x 1hour seminars
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

#### Learning outcomes

On completion of this module, a student should be able to:
• discretize elliptic boundary value problems in an efficient way;
• derive accurate numerical solutions of elliptic boundary value problems;
• explain and use spectral methods and spectral element methods.

#### Brief description

Boundary value problems, in ordinary and partial differential equations, occur naturally in science and engineering, eg clamped beam problems, slow viscous flow, and elasticity. Over the centuries many famous mathematicians have been challenged by such problems and have produced elegant classical solution methods. Today it is possible to marry some of these classical discoveries with modern computational methods, to enable the solution of contemporary problems.

#### Aims

To teach students how to solve linear boundary problems using modern analytic and computational methods.

#### Content

1. TWO POINT BOUNDARY VALUE PROBLEMS: Variational and weak formulations.
2. GALERKIN AND PSEUDOSPECTRAL GALERKIN METHODS: Pseudospectral Galerkin and collocation methods.
3. ERROR ESTIMATE AND CONVERGENCE RATES FOR FINITE DIMENSIONAL APPROXIMATIONS
4. ELLIPTIC BOUNDARY VALUE PROBLEMS IN THE PLANE: Approximation in Tensor Product Spaces of Polynomials
5. INTRODUCTION TO ELEMENT METHODS.

Books
** Supplementary Text
C Johnson (1987) Numerical Solution of Partial Differential Equations by the Finite Element Method Cambridge University Press 0521347580
D Funaro (1992) Polynomial Approximation of Differential Equations Springer Verlag 3540552308

#### Notes

This module is at CQFW Level 7