Unit name | Numerical Methods for Partial Differential Equations |
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Unit code | MATHM0011 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Professor. Kerswell |
Open unit status | Not open |
Pre-requisites |
MATH20700 (Numerical Analysis 2) and MATH20402 (Applied Partial Differential equations 2) or by permission for graduate students who have taken the equivalent elsewhere. |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Partial differential equations (PDEs) are ubiquitous in modelling physical systems but are not generally solvable in closed form. This unit will discuss some of the numerical methods used to approximate the solutions of some generic PDEs. Topics will include finite difference methods (spatial discretisation, accuracy, stability and convergence, dissipation and dispersion), spectral methods (approximation theory, Fourier series and periodic problems, Chebyshev polynomial and non-periodic problems, Galerkin, collocation and Tau techniques, convolutions and fast transforms) plus others as time allows (e.g. the boundary element method, Krylov-based iterative methods, branch continuation methods, finite element methods).
The aims of this unit are to provide an introduction to a variety of numerical methods for solving partial differential equations. The emphasis will be on understanding the fundamentals: the appropriateness of a given method for a given type of PDE (elliptic, parabolic, hyperbolic) and how to construct an accurate and stable numerical scheme to produce answers of the required precision.
A student successfully completing this unit will be able to:
The unit will be delivered through lectures. The lectures will be transmitted over the internet as part of the Taught Course Centre (TCC). The TCC is a consortium of five mathematics departments, including Bath, Bristol, Imperial College, Oxford and Warwick.
Formative homework exercises will be assigned throughout the unit.
The final assessment mark will be based on a 1½-hour written examination (100%).