Postgraduate Course: Numerical Techniques of Partial Differential Equations (MATH11068)
|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
|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 delivered by Heriot Watt University and is only available to students on the MSc Financial Mathematics programme.
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.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| MSc Financial Mathematics students only.
Course Delivery Information
|Academic year 2017/18, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
Lecture Hours 20,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Additional Information (Learning and Teaching)
Examination takes place at Heriot-Watt University.
|Assessment (Further Info)
|Additional Information (Assessment)
||See 'Breakdown of Assessment Methods' and 'Additional Notes' above.
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Numerical Techniques of Partial Differential Equations (MATH11068) ||2:00|
| 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.
|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.
|Graduate Attributes and Skills
|Course organiser||Dr David Siska
Tel: (0131 6)51 9091
|Course secretary||Ms Hannah Burley
Tel: (0131 6)50 4885