|| MA34710 |
|| NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS |
|| 2006/2007 |
|| Mr Alan Jones |
|| Intended for use in future years |
|Next year offered
|| N/A |
|Next semester offered
|| N/A |
|| Professor Russell Davies |
|| MA25110 |
|| MA30210 |
| Course delivery
|| Lecture || 19 x 1 hour lectures |
|| Seminars / Tutorials || 3 x 1 hour example classes |
|Assessment Type||Assessment Length/Details||Proportion|
|Semester Exam||2 Hours (written examination) ||100%|
|Supplementary Assessment||2 Hours (written examination) ||100%|
On completion of this module, a student should be able to:
1. discretise an elliptic partial differential equation using and finite element methods;
2. perform an error analysis for the discrete approximation to elliptic equations;
3. discretise hyperbolic and parabolic partial differential equations in one space variable;
perform an error analysis for the discrete approximation to hyperbolic and parabolic equations.
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, hyperbolic and parabolic type. Concepts such as consistency, convergence and stability of numerical methods will be discussed. Fourier methods will be used to analyse stability and convergence of finite difference methods, while finite element methods will be analysed in terms of interpolation error estimates.
1. Variational formulation and the finite element method. Finite element spaces and interpolation.
2. Finite difference approximations to hyperbolic and parabolic partial differential equations in one space variable. Local truncation error and error analysis. Explicit and implicit methods. Convergence and stability. The Thomas algorithm.
** Recommended Text
Johnson, Claes (1987.) Numerical solution of partial differential equations by the finite element method /Claes Johnson.
Strikwerda, J C Finite difference schemes and PDE's
Strikwerda, John C. (1989.) Finite difference schemes and partial differential equations /John C.Strikwerda.
Brooks-Cole Publishing Co,
** Supplementary Text
K W Morton and D F Mayers (1994) Numerical Solution of Partial Differential Equations
2001 reprint. Cambridge University Press 0521429226
This module is at CQFW Level 6