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 1A (weeks 1 - 6) |
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 |
Unit aims
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.
General Description of the Unit
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)
NOTE: This unit is also part of the Oxford-led Taught Course Centre (TCC), and is taken by first- and second-year PhD students in Bristol and its TCC partner departments. The unit has been designed primarily with a postgraduate audience in mind. Undergraduate students should not normally take more than one TCC unit per semester.
Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/
A student successfully completing this unit will be able to:
Transferable Skills
Computational techniques; interpretation of computational results; relation of numerical results to mathematical theory.
The unit will be delivered through lectures.
100% Examination.
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.