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   Applications accepted all year round  Competition Funded PhD Project (Students Worldwide)

About the Project

A common procedure for the numerical solution of partial differential equations is the method of lines, which results in a large system of ordinary differential equations. These ordinary differential equations are often stiff, and thus implicit methods are commonly used to solve them.

However, implicit methods are costly because they solve a system of (algebraic) equations at every step. Exponential integrators provide an alternative. They are constructed using the (matrix) exponential; hence the name. The matrix exponential is the exact solution of a linear equation and thus a good building block for numerical methods. Unfortunately, computing the matrix exponential is expensive and special algorithms are needed for large matrices.

The aim of this project is to investigate methods to compute the matrix exponential, how to incorporate them in exponential integrators, and to implement this. This project requires some prior knowledge of numerical analysis (numerical linear algebra and numerical methods for differential equations) and some programming experience.

Funding Notes

A highly competitive EPSRC Doctoral Training Partnership Studentship consisting of the award of fees with a maintenance grant (currently £16,062 per year for session 2022/23) for 3.5 years. This opportunity is open to all applicants. All candidates will be placed into the EPSRC Doctoral Training Partnership Studentship Competition and selection is based on academic merit. Please visit our website for further information.

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