MA34710 - NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

Module Identifier

MA34710

Module Title

NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

Academic Year

2003/2004

Co-ordinator

Professor Tim Phillips

Semester

Semester 2

Other staff

Professor Russell Davies

Pre-Requisite

MA25110

Course delivery

Lecture

19 x 1 hour lectures

Seminars / Tutorials

3 x 1 hour example classes

Assessment

Assessment Type	Assessment Length/Details	Proportion
Semester Exam	2 Hours (written examination)	100%
Supplementary Assessment	2 Hours (written examination)	100%

Learning outcomes

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

discretise an elliptic partial differential equation using finite difference and finite elements methods.
perform an error analysis for the discrete approximation to elliptic equations.
solve the discrete equations using classical iterative methods.
analyse the convergence behaviour of these iterative methods.
discretise parabolic partial differential equations in one space variable.
perform an error analysis for the discrete approximation to parabolic equations.

Brief description

Partial differential equations are the main means of providing mathematical models in science, engineering and other fields. Generally these models must be solved numerically. This course provides an introduction to numerical techniques for eliiptical and parabolic equations.

Aims

The aim of this course is to provide an introduction to numerical methods for solving partial differential equations of elliptic and parabolic type. Concepts such as consistency, convergence and stability of numerical methods will be discussed. Classical iterative methods for solving the systems of linear algebraic equations arising from the discretization of elliptic problems will be described and their convergence behaviour analysed.

Content

Finite difference approximations to elliptic partial differential equations. Local truncation error and error analysis. Boundary conditions on a curved boundary. Variational formulation and the finite element method. Classical iterative methods for solving linear systems of algebraic equations: Jacobi, Gauss-Seidel, SOR. Fourier analysis of convergence.
Finite difference approximations to parabolic partial differential equations in one space variable. Local truncation error and error analysis. Explicit and implicit methods. Convergence and stability. The Thomas algorithm.

Reading Lists

Books
** Recommended Text
K W Morton and D F Mayers (1994) Numerical Solution of Partial Differential Equations 2001 reprint. Cambridge University Press 0521429226
G D Smith (1985) Numerical Solution of Partial Differential Equations: Finite Difference Methods 3rd. Oxford University Press 0198596413

Notes

This module is at CQFW Level 6