Module Identifier MA34710  
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 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:

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.


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.


  1. 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.
  2. 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

** 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


This module is at CQFW Level 6