School of Mathematical & Statistical Sciences Faculty Publications and Presentations

A Petrov–Galerkin spectral method for the numerical simulation and analysis of fractional anomalous diffusion

Document Type

Article

Publication Date

1-2021

Abstract

Anomalous diffusion problems are used to describe the evolution of particle's motion in crowded environments with many applications, such as modeling the intracellular transport and disordered media. In the present paper, we develop a Petrov–Galerkin spectral method for the fourth-order anomalous fractional diffusion equations. For the dimension reduction, we use a discretization in time by the convolution quadrature. We then introduce the basis sets for the trial-and-test spaces using modal Bernstein basis functions with a presentation of the method in a weak spectral formulation along with a discussion of the structure of the resulting systems, the convergence, and stability of the proposed method. The theoretical results are supported by illustrating some numerical examples.

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© 2020 John Wiley & Sons, Ltd.

https://onlinelibrary.wiley.com/share/SJBYFXCNMBSIMAFKF5FX?target=10.1002/mma.6908

Publication Title

Mathematical Methods in the Applied Sciences

DOI

10.1002/mma.6908

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