Course co-ordinator(s): Dr Stefan Klus (Edinburgh).
Aims:
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.
Summary:
In this course we will cover the following topics:
- 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.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Edinburgh.
Learning Outcomes: Subject Mastery
On completion of the 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.
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.
SCQF Level: 11.
Credits: 7.5.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.
Canvas: further information and course materials are available on Canvas