Modified BDF2 schemes for subdiffusion models with a singular source term
Numerical Analysis
2022-07-19 v1 Numerical Analysis
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 -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.
Cite
@article{arxiv.2207.08447,
title = {Modified BDF2 schemes for subdiffusion models with a singular source term},
author = {Minghua Chen and Jiankang Shi and Zhi Zhou},
journal= {arXiv preprint arXiv:2207.08447},
year = {2022}
}
Comments
25pages