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Mathematics > Numerical Analysis

arXiv:2207.08447 (math)
[Submitted on 18 Jul 2022]

Title:Modified BDF2 schemes for subdiffusion models with a singular source term

Authors:Minghua Chen, Jiankang Shi, Zhi Zhou
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Abstract:The aim of this paper is to study the time stepping scheme for approximately solving the subdiffusion equation with a weakly singular source term. In this case, many popular time stepping schemes, including the correction of high-order BDF methods, may lose their high-order accuracy. To fill in this gap, in this paper, we develop a novel time stepping scheme, where the source term is regularized by using a $k$-fold integral-derivative and the equation is discretized by using a modified BDF2 convolution quadrature. We prove that the proposed time stepping scheme is second-order, even if the source term is nonsmooth in time and incompatible with the initial data. Numerical results are presented to support the theoretical results.
Comments: 25pages
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2207.08447 [math.NA]
  (or arXiv:2207.08447v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2207.08447

Submission history

From: Minghua Chen Professor [view email]
[v1] Mon, 18 Jul 2022 09:00:07 UTC (34 KB)
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