Course Information Undergraduate prospectus

Numerical Solution of PDEs

Course summary

Course code: MATH0060
Level: 6
Credits: 15
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Yvonne Fryer

Specification

Pre and co requisites

Linear Algebra and Applications

Aims

The computational modelling of real world problems relies heavily on the numerical solution of partial differential equations (PDEs), especially in industrial, environmental, engineering and scientific areas. Graduates need an understanding of modern methods and an awareness of the problems involved in obtaining numerical solutions.

Learning outcomes

By the end of the course, students should be able to:
A. identify appropriate solution procedures for a given PDE;
B. derive and implement finite difference schemes for PDEs;
C. apply the finite volume method to elliptic PDEs;
D. appreciate the potential sources of error in numerical methods for PDEs.

Indicative content

Classification of PDEs: elliptic, parabolic and hyperbolic equations.
Finite difference schemes: derivation and implementation for all classes of PDE.
Finite volume methods: derivation and implementation for elliptic problems.
Finite element methods: background and example software.
Accuracy, stability and error control.
The use of numerical PDE solutions in industry.

Teaching and learning activity

Concepts and methods will be introduced and demonstrated in lectures. Students will learn to derive numerical schemes in tutorial work and implement them in software during laboratory-based classes.

Learning Time (1 credit = 10 hours).

Scheduled contact hours:
Note: include in scheduled time: project supervision, demonstrations, practical classes and workshops, supervised time in studio or workshop, scheduled lab work, fieldwork, external visits, work-based learning where integrated into a structured academic programme.
lectures 26;
seminars;
supervised practical sessions;
tutorials 13;
examination 3;
other scheduled time.

Guided independent study:
Note: include in guided independent study preparation for scheduled sessions, follow up work, wider reading or practice, revision.
Independent coursework 25;
Independent laboratory work 10;
other non-scheduled time 73.

Placements (including work placement and year abroad).

Total hours ('Should be equal to credit x 10') 150.


Assessment

Coursework - 50%
Coursework covering learning outcomes, which may include selected tutorial work.

Examination - 50%
Examination of 3 hours in duration covering learning outcomes
Last item of assessment.