Spring

Unit(s) of Assessment	Weighting Towards Module Mark( %)
50 minute class test	12
MATLAB coursework	13
2 hour unseen examination	75
Qualifying Condition(s)  An aggregate mark of 40% is required to pass this module.

Partial differential equations (PDEs) may be used to model many physical/biological processes.  In MS302/MS211 some methods for solving PDEs were introduced.  However, many PDEs cannot be easily solved by hand and computational techniques play an important role in understanding and interpreting the behaviour of a given PDE.  

In this module we examine some numerical methods for solving PDEs including the theory that underlies them and their application.

MAT2001 Numerical and Computational Methods

MAT2011 Linear PDEs

The aim of the module is to introduce the basic principles behind applying finite difference methods, finite element methods and spectral methods to solve partial differential equations.

By the end of the course students should:

    * know how to apply some numerical methods to solve partial differential  
      equations

    * be able to write MATLAB code to solve simple cases.
    * understand the notions of convergence, accuracy and stability for the 
      methods that they learn.

The content of the lectures will include:

    * Finite differences methods in general, there derivation and the notions
      of accuracy, consistency and stability.

    *  Specific finite difference methods for parabolic partial differential
       equations including Euler's method, the theta method and the Crank-
       Nicolson method.

    * Specific finite difference methods for hyperbolic partial differential 
      equations including upwind schemes, the leapfrog method and the 
      Lax Wendroff method. The Lax Equivalence Theorem will be 
      discussed.

    *  Finite element methods for elliptic partial differential equations.

    * Spectral method with  Fast Fourier Transform for Burgers’ equation.

    * An important part of the course will be the hands on experience of 
      writing and running code to solve partial differential equations. For this
      purpose MATLAB will be used and the basics of how to use MATLAB
      will be taught.

Teaching is by lectures, tutorials and computer laboratory sessions. Learning takes place through the lectures, reading through lecture notes and textbooks, tutorials, working through example sheets and the computing laboratory sheets.

3 lectures/tutorial hours per week. At least one of these sessions every fortnight will be held in a computing laboratory.

G.D. Smith, Numerical Solution of Partial Differential Equations, OUP 2003.

7 January 2010