Mathematics
Te Tari Pāngarau me te Tatauranga
Department of Mathematics & Statistics

MATH4PD Numerical Solution of PDEs

First Semester
10 points
 

Not offered in 2016

While analytic solutions to partial differential equations (PDEs) — e.g. Fourier series, integral transforms, Green’s functions — coupled with qualitative analysis — e.g. maximum principles, asymptotic behaviour — provide essential insights into mathematical models, most realistic models require numerical solutions. Applications are numerous and range from modelling astrophysical detonations (shocks), elastic deformations (e.g. seismic waves) and fluid flow (e.g. subsurface flow–groundwater, geothermal) to medical and geophysical imaging.

The aim of the course is to give a broad introduction to numerical methods for solving PDEs, and prepare you for graduate studies in applied mathematics. We will cover the major methods. By the end of the course you should be able to code your own schemes for 1 and 2-D problems, and be able to analyse convergence and stability. A first course on PDEs is essential, and some exposure to Matlab and linear algebra will be required. Background in analysis would be advantageous, will help you appreciate the core ideas behind numerical techniques, and put you in a better position to carry out independent work.

We aim to cover the following topics:

We may, if time permits, explore some of the following topics:

Learning will be hands on, and homework will consist, in the main, of Matlab based mini-projects.

Prerequisites

Linear Algebra (MATH 202) and Partial Differential Equations (MATH 304) or equivalent

Lecturer

Nick Dudley Ward (Physics department, phone 479 7808, email: nick.dudleyward@otago.ac.nz)

(Nick is director of the Otago Computational Modelling Group (OCMO), www.ocmo.co.nz)

Internal Assessment

There will be assignments and a project. Details to come...

Final exam

Details to come...

Final mark

While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.