Module Identifier MAM4420  
Module Title BOUNDARY VALUE PROBLEMS  
Academic Year 2001/2002  
Co-ordinator Professor Arthur Davies  
Semester Semester 2  
Other staff Professor T Phillips  
Pre-Requisite MA30210 , MA34110 , MA34410  
Course delivery Lecture   20 x 1hour lectures  
  Seminars / Tutorials   7 x 1hour seminars  
Assessment Exam   2 Hours (written examination)   100%  
  Resit assessment   2 Hours (written examination)   100%  

General 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.

Learning outcomes


On completion of this module, a student should be able to:

Syllabus


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.

Reading Lists

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