Numerical Solution of Differential Equations - MA587

Location Term Level Credits (ECTS) Current Convenor 2018-19
Canterbury Autumn
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6 15 (7.5) DR A Deano Cabrera

Pre-requisites

For delivery to students completing Stage 1 before September 2016:
Pre-requisite: MA552 (Analysis), MA553 (Linear Algebra)
Co-requisite: None

For delivery to students completing Stage 1 after September 2016:
Pre-requisite: MAST5005 (Linear Partial Differential Equations), MAST5009 (Numerical Methods), MAST5012 (Ordinary differential equations)
Co-requisite: None

Restrictions

None

2018-19

Overview

Most differential equations which arise from physical systems cannot be solved explicitly in closed form, and thus numerical solutions are an invaluable way to obtain information about the underlying physical system. The first half of the module is concerned with ordinary differential equations. Several different numerical methods are introduced and error growth is studied. Both initial value and boundary value problems are investigated. The second half of the module deals with the numerical solution of partial differential equations. The syllabus includes: initial value problems for ordinary differential equations; Taylor methods; Runge-Kutta methods; multistep methods; error bounds and stability; boundary value problems for ordinary differential equations; finite difference schemes; difference schemes for partial differential equations; iterative methods; stability analysis.

Details

This module appears in:


Contact hours

42

Method of assessment

80% Examination, 20% Coursework

Indicative reading

Burden, R.L., and Faires, J.D., and Burden, A. M., Numerical Analysis, 10th edition, Cengage Learning, 2016
Iserles, A first course in the numerical analysis of differential equations, 2nd edition, Cambridge University Press, 2009
Morton, K. W. and Mayers, D.F., Numerical solution of partial differential equations: an introduction, Cambridge University Press, 2011

See the library reading list for this module (Canterbury)

See the library reading list for this module (Medway)

Learning outcomes

The intended subject specific learning outcomes.
On successfully completing the module students will be able to:
1 demonstrate systematic understanding of key aspects of finite difference methods for approximating solutions of ordinary differential equations (ODEs) and partial differential equations (PDEs);
2 demonstrate the capability to deploy established approaches accurately to analyse and solve problems using a reasonable level of skill in calculation and manipulation of the material in the following areas: multistep methods, approximation of boundary value problems for ODEs, discretization of PDEs, error and stability analysis, elementary numerical linear algebra;
3 apply key aspects of finite difference methods in well-defined contexts, showing judgement in the selection and application of tools and techniques;
4 show judgement in the selection and application of Matlab commands to implement numerical methods.

The intended generic learning outcomes.
On successfully completing the module students will be able to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make competent use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.

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