|| MA34710 |
|| NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS |
|| 2004/2005 |
|| Professor Tim Phillips |
|| Semester 2 |
|| Professor Russell Davies |
|| MA25110 |
| 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:
discretise an elliptic partial differential equation using finite difference and finite elements methods.
perform an error analysis for the discrete approximation to elliptic equations.
solve the discrete equations using classical iterative methods.
analyse the convergence behaviour of these iterative methods.
discretise parabolic partial differential equations in one space variable.
perform an error analysis for the discrete approximation to 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 and parabolic type. Concepts such as consistency, convergence and stability of numerical methods will be discussed. Classical iterative methods for solving the systems of linear algebraic equations arising from the discretization of elliptic problems will be described and their convergence behaviour analysed.
1. Finite difference approximations to elliptic partial differential equations. Local truncation error and error analysis. Boundary conditions on a curved boundary. Variational formulation and the finite element method. Classical iterative methods for solving linear systems of algebraic equations: Jacobi, Gauss-Seidel, SOR. Fourier analysis of convergence.
2. Finite difference approximations to 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
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,
Johnson, Claes (1987.) Numerical solution of partial differential equations by the finite element method /Claes Johnson.
** 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