Efficient numerical approximation of a non-regular Fokker-Planck equation associated with first-passage time distributions
type: Item
instance of: scholarly article
title: Efficient numerical approximation of a non-regular Fokker-Planck equation associated with first-passage time distributions
author: Udo Boehm
author: Sonja Cox
author: Gregor Gantner
author: Rob P. Stevenson
published in: BIT
publication date: 2022-11-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/2103.04839
review text: The Fokker-Planck equation on a one-dimensional spatial domain with discontinuity between initial and boundary data and time-dependent boundaries is solved numerically. The equation is transformed first into an equation on a rectangular time-space domain. It was shown that the solution of a corresponding equation with a suitable constant drift function, whose solution is explicitly available as a fast converging series expansion, captures the singularity present in the solution for a variable drift function. The equation for the difference of both these solutions, which is thus more regular than both terms, is solved with a minimal residual method. In order to efficiently solve Fokker-Planck equations that depend on multiple parameters, the authors apply a sparse tensor product interpolation method that can be shown to converge at a subexponential rate as a function of the number of interpolation points. The predicted convergence rates of the minimal residual method and that of the interpolation method are supported by numerical simulations.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K08
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35Q84
zbMATH DE Number: 7621789
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: time-dependent spatial domain
zbMATH Keywords: space-time variational formulation
zbMATH Keywords: parameter-dependent PDE
zbMATH Keywords: sparse tensor product interpolation
reviewed by: Bülent Karasözen
MaRDI profile type: Publication
OpenAlex ID: W3134181220
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DOI: 10.1007/S10543-022-00914-2
description: scientific article; zbMATH DE number 7621789