# NUMERICAL SOLUTION OF PDES - 2022/3

Module code: MAT3015

Module Overview

Partial differential equations (PDEs) may be used to model many physical and biological processes.  Although there are some analytical solutions available for PDEs, many PDEs cannot be easily solved by hand and computational techniques play an important role in understanding and interpreting the behaviour of a given PDE.

In this module some numerical methods for solving PDEs are examined, including underlying theory and their application.

Module provider

Mathematics

DOUGLAS Natalie (MathsMaths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 6

JACs code: G100

Module cap (Maximum number of students): N/A

Independent Learning Hours: 117

Lecture Hours: 25

Laboratory Hours: 8

Module Availability

Semester 2

Prerequisites / Co-requisites

MAT2001 Numerical and Computational Methods MAT2011 Linear PDEs

Module content

The module will include the following:

• Finite difference methods – derivation, notions of accuracy, consistency and stability.

• Euler's method; the theta method; and the Crank-Nicolson method.

• The leapfrog method; the Lax Wendroff method; and the Lax Equivalence Theorem.

• Finite element methods, spectral methods.

• Gaining experience of writing and running code to solve partial differential equations using MatLab.

Assessment pattern

Assessment type Unit of assessment Weighting
Coursework COURSEWORK 20
Examination EXAMINATION - 2 HOURS 80

Alternative Assessment

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

·         Subject knowledge through the recall of key definitions, theorems and methods.

·         Analytical ability through the solution of unseen problems in the test and exam.

·         Practical programming through the solution of guided problems in coursework.

Thus, the summative assessment for this module consists of:

·         One two hour examination (two of three best answers contribute to exam mark) at the end of Semester 1; worth 80% module mark.

·         One coursework; worth 20% module mark.

Formative assessment and feedback

Students receive written feedback via two marked unassessed coursework assignments over an 11 week period.  In addition, verbal feedback is provided by lecturer/class tutor.

Module aims

• The aim of this module is to introduce the basic principles behind applying finite difference methods and finite element methods to solve partial differential equations.

Learning outcomes

Attributes Developed
1 Know how to apply numerical methods to solve partial differential equations KC
2 Be able to write MatLab code to solve simple cases. KCPT
3 Understand the notions of convergence, accuracy and stability. KC

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A detailed introduction to numerical methods and their analysis.

• Experience (through demonstration) of the methods used to analyse, understand and solve problems involving numerical methods.

The learning and teaching methods include:

• 25 lectures/tutorials, 8 labs.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.