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Mathematics > Numerical Analysis

arXiv:2205.10971 (math)
This paper has been withdrawn by Xiangong Tang
[Submitted on 23 May 2022 (v1), last revised 8 Jun 2022 (this version, v3)]

Title:Numerical method for the Fokker-Planck equation of Brownian motion subordinated by inverse tempered stable subordinator with drift

Authors:Xiangong Tang, Can Wang, Weihua Deng
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Abstract:In this work, based on the complete Bernstein function, we propose a generalized regularity analysis including maximal $\mathrm{L}^p$ regularity for the Fokker--Planck equation, which governs the subordinated Brownian motion with the inverse tempered stable subordinator that has a drift. We derive a generalized time--stepping finite element scheme based on the backward Euler convolution quadrature, and the optimal-order convergence of the numerical solutions is established using the proven solution regularity. Further, the analysis is generalized to more general diffusion equations. Numerical experiments are provided to support the theoretical results.
Comments: Uploaded without the consent of the tutor, so request to withdraw
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2205.10971 [math.NA]
  (or arXiv:2205.10971v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2205.10971

Submission history

From: Xiangong Tang [view email]
[v1] Mon, 23 May 2022 00:31:36 UTC (35 KB)
[v2] Mon, 30 May 2022 23:26:06 UTC (31 KB)
[v3] Wed, 8 Jun 2022 01:38:15 UTC (1 KB) (withdrawn)
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