# Gwybodaeth Modiwlau

Module Identifier
MA34710
Module Title
Numerical Solution of Partial Differential Equations
2019/2020
Co-ordinator
Semester
Semester 2
Pre-Requisite
MA25220 or MA34110 or MT25220, or MT34120
External Examiners
• Dr Andrew Hazel (Reader - University of Manchester)

Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Lecture 12 x 1 Hour Lectures
Practical 5 x 2 Hour Practicals

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   50%
Semester Assessment Report 1  on numerical implementation of the finite difference method (2000 words).  25%
Semester Assessment Report 2  on numerical implementation of the finite difference method (2000 words).  25%
Supplementary Exam 2 Hours   100%

### Learning Outcomes

On successful completion of this module students should be able to:

1. Discretise elliptic, hyperbolic and parabolic partial differential equations using finite difference methods.

2. Use the variational formulation to derive a finite element discretisation of a PDE.

3. Perform an error and convergence analysis for these discrete approximations to PDEs.

4. Solve an elliptic or parabolic PDE numerically using different computational methods.

### Brief description

This module provides 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.

### Content

Finite difference approximations to elliptic, hyperbolic and one-dimensional parabolic partial differential equations. Local truncation error and error analysis.

Variational formulation and the finite element method. Convergence and stability.

Numerical implementation of these methods.

### Module Skills

Skills Type Skills details
Application of Number Inherent in module.
Communication The written reports will require students to clearly explain their findings.
Improving own Learning and Performance Problem sheets will allow students to assess their progress.
Personal Development and Career planning Familiarity with numerical methods for solving differential equations is a valuable career skill, particularly for those going on to work in finance and in industry.
Problem solving Inherent in module.
Subject Specific Skills Inherent in module.
Team work Students will be encouraged to work in groups for the practical sessions.

### Notes

This module is at CQFW Level 6