[School of Natural Sciences PhD Scholarships] Numerical approximations of fractional differential equations and their applications

About the project

About the Project In the past few decades, traditional differential equations with diffusion driven by Brownian motions might no longer give an accurate description of many social and natural phenomena with memory effects or long-range interactions. Fractional type derivatives, as an alternative to classical integer order derivatives, are employed more frequently after these more exotic complex systems are modelled. However, the resulting equations are increasingly more difficult to solve with few exact solutions available, and numerical solutions are usually the only viable approach. In this project, novel finite difference methods will be used to solve related differential equations, usually with the presence of a fractional Laplacian operator (the fractional power of the standard negative Laplace operator). The methods will be adapted according to the particular context they will be solved, like pattern formation, singularity formation and asymptotic limits. This project is expected to start in September 2027. Before you apply: We strongly recommend that you contact the supervisors for this project before you apply. How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships . If you don’t already have an applicant account, please follow the instructions here . When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications . Please note late or incomplete applications will not be considered. Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status. We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder. Eligibility : The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in a relevant science or engineering discipline OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in a relevant science or engineering discipline. This project will remain open until filled. If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026. If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

Research areas