Postgraduate Course: Numerical Techniques of Partial Differential Equations (MATH11068)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 7.5 |
ECTS Credits | 3.75 |
| Summary | 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.
This course is only available to students on the MSc Financial Mathematics programme. |
| Course description |
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.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | MSc Financial Mathematics students only. |
Course Delivery Information
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| Academic year 2015/16, Not available to visiting students (SS1)
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Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| 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 )
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| Additional Information (Learning and Teaching) |
Examination takes place at Heriot-Watt University.
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| Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
See 'Breakdown of Assessment Methods' and 'Additional Notes' above. |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
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| Main Exam Diet S2 (April/May) | Numerical Techniques of Partial Differential Equations (MATH11068) | 2:00 | |
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.
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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.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | PDEs |
Contacts
| Course organiser | Dr Sotirios Sabanis
Tel: (0131 6)50 5084
Email: |
Course secretary | Mr Brett Herriot
Tel: (0131 6)50 4885
Email: |
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