Transient numerical approximation of hyperbolic diffusions and beyond

Leonenko, G. ORCID: https://orcid.org/0000-0001-8025-661X and Phillips, T. N. ORCID: https://orcid.org/0000-0001-6455-1205 2023. Transient numerical approximation of hyperbolic diffusions and beyond. Journal of Computational and Applied Mathematics 422 , 114893. 10.1016/j.cam.2022.114893

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Abstract

In this paper different types of hyperbolic diffusions and their corresponding transient Fokker–Planck equation are described and numerical solutions are presented. Diffusion models were developed that can fit both the marginal distribution and correlation structure and they have found a wide application in finance, turbulence and environmental time series. Hyperbolic diffusions have a complicated structure and variety of parameters and are extremely difficult to study and to model. We propose a numerical technique that solves one-dimensional hyperbolic Fokker–Planck equation in time dependent case. Note that this is a first study where transient hyperbolic diffusions are considered. The numerical technique is based on adaptive reduced basis method with spectral element discretization. It involves enrichment and projection stages where an optimal basis is found in a dynamic way using the singular value decomposition (SVD). The approach dramatically reduces the number of degrees of freedom required to solve the problem. The numerical evaluations of the Fokker–Planck equation are verified with available stationary solutions.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Medicine Mathematics
Publisher:	Elsevier
ISSN:	0377-0427
Date of First Compliant Deposit:	13 October 2022
Date of Acceptance:	5 October 2022
Last Modified:	22 Nov 2024 01:15
URI:	https://orca.cardiff.ac.uk/id/eprint/153364

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