Efficient numerical methods for the solution of fractional differential equations

Summary

Fractional differential equations are a generalisation of differential equations which involve derivatives of non-integer order. These equations are known for their ability to model memory and hereditary properties of various materials and processes. However, their solution poses significant numerical challenges due to the non-local nature of fractional derivatives.

This project aims to address computational challenges associated with fractional calculus, which has applications in various scientific and engineering disciplines, including viscoelasticity, anomalous diffusion, medical ultrasound and financial mathematics.

The ideal candidate will have a some experience in scientific computing in the context of partial differential equations, e.g. using finite element, finite difference or spectral methods. Prior experience with fractional calculus specifically is not required.

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study in the School of Computer Science is an IELTS of 6.5 overall with at least 6.5 in writing and at least 6.0 in reading, listening and speaking or equivalent. The test must be dated within two years of the start date of the course in order to be valid.