James Hoult
Visiting Lecturer
In 2016, I earned a first-class degree in Mathematics, followed by a Master's degree with distinction in the same field from the University of Chester in 2018. I began my PhD studies at Chester in 2021, focusing on various aspects of Mathematics. My primary research interests revolve around Stochastic Fractional Differential Equations, Stochastic Partial Differential Equations, and Numerical Analysis. To approximate these models, I apply various techniques, including the Finite Difference scheme, the central difference method, and piecewise constant functions.
At present, I am working on my fourth publication, which explores a more intricate Stochastic Fractional Differential Equation with weakly singular kernels. This research delves into interesting error estimates and stability properties, which have been validated using a numerical L1 scheme. To date, I have successfully published three papers, which are listed below:
- Spatial discretization for stochastic semi-Linear subdiffusion equations driven by fractionally integrated multiplicative space-time white noise (2021)
- Spatial Discretization for Stochastic Semilinear Superdiffusion Driven by Fractionally Integrated Multiplicative Space–Time White Noise (2023)
- Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise (2024)
I began my role as a Visiting Lecturer in 2022, focusing on Pure Mathematics, while also assisting Dimitra with various responsibilities. Presently, I am teaching course MA5005 and will be continuing this next year. With extensive teaching experience under my belt, I provide private tutoring to numerous students one-on-one in the Chester area, having worked with over 100 students for more than seven years.
My primary focus of research focuses on the numerical analysis of Stochastic Fractional Partial Differential Equations (PDEs), particularly examining equations related to sub-diffusion and super-diffusion with additive and multiplicative noise. Additionally, I am working towards publishing another paper that explores Stochastic Fractional Differential Equations characterized by weakly singular kernels.
- Spatial discretization for stochastic semi-Linear subdiffusion equations driven by fractionally integrated multiplicative space-time white noise (2021)
- Spatial Discretization for Stochastic Semilinear Superdiffusion Driven by Fractionally Integrated Multiplicative Space–Time White Noise (2023)
- Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise (2024)
Visiting Lecturer in Mathematics
University of Chester
November 2022 – Present