Postgraduate Course: Numerical Techniques of Partial Differential Equations (MATH11068)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Not available to visiting students |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Credits | 7.5 |
| Home subject area | Mathematics |
Other subject area | Financial Mathematics |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | The aim of this course is to introduce students to numerical techniques for solving PDEs. For financial applications the need is for the diffusion equation and for free boundary value problems. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | MSc Financial Mathematics students only. |
| Additional Costs | None |
Course Delivery Information
|
| Delivery period: 2013/14 Semester 2, Not available to visiting students (SS1)
|
Learn enabled: No |
Quota: None |
Web Timetable |
Web Timetable |
| Course Start Date |
13/01/2014 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
75
(
Lecture Hours 20,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
51 )
|
| Additional Notes |
Examination takes place at Heriot-Watt University.
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| No Exam Information |
Summary of Intended Learning Outcomes
On completion of this course the student should be able to:
- Understand the techniques outlined above
- implement these numerical methods using a suitable computer package
- hold a critical understanding of modern numerical techniques for solving PDEs
- have a conceptual understanding of the relation between consistency, stability and convergence in numerical schemes
- understand the explicit, implicit and Crank-Nicolson finite difference methods for solving one-dimensional PDEs
- compute numerical solutions for simple problems involving PDEs
- demonstrate a knowledge of some methods for solving higher dimension PDEs
- find problem solutions in groups
- plan and organize self-study and independent learning
- implementation of numerical methods using a suitable computer package such as Matlab
- communicate effectively problem solutions to peers. |
Assessment Information
| See 'Breakdown of Assessment Methods' and 'Additional Notes' above. |
Special Arrangements
| MSc Financial Mathematics students only. |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Finite difference methods for parabolic initial value problems : stability, consistency and convergence.
Local truncation error, von Neumann (Fourier) stability method.
Explicit, implicit and Crank-Nicolson methods for the one-dimensional diffusion equation.
Matrix version of numerical schemes; multi-level schemes for the heat equation.
Introduction to more general parabolic PDE¿s.
ADI methods for two-dimensional problems.
|
| Transferable skills |
Not entered |
| Reading list |
Iserles, A. (1996). A First Course in the Numerical Analysis of Differential Equations. CUP.
Smith, G. (1985). Numerical Solution of Partial Differential Equations: Finite Difference Methods. OUP.
|
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | PDEs |
Contacts
| Course organiser | Dr Sotirios Sabanis
Tel: (0131 6)50 5084
Email: S.Sabanis@ed.ac.uk |
Course secretary | Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk |
|
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