# Gwybodaeth Modiwlau

Module Identifier
MA34710
Module Title
Numerical Solution of Partial Differential Equations
Academic Year
2013/2014
Co-ordinator
Semester
Intended for use in future years
Co-Requisite
Pre-Requisite
Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Lecture 19 x 1 hour lectures
Seminars / Tutorials 3 x 1 hour example classes

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (written examination)  100%
Supplementary Assessment 2 Hours   (written examination)  100%

### Learning Outcomes

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.

### Brief description

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.

### Aims

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.

### Content

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.

### Notes

This module is at CQFW Level 6