TY - JOUR
T1 - Modified BDF2 Schemes for Subdiffusion Models with a Singular Source Term
AU - Chen , Minghua
AU - Shi , Jiankang
AU - Zhou , Zhi
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 897
EP - 924
PY - 2025
DA - 2025/08
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1039
UR - https://global-sci.org/intro/article_detail/ijnam/24297.html
KW - Subdiffusion, modified BDF2 schemes, singular source term, error estimate.
AB - <p style="text-align: justify;">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 an $m$-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. The proposed
approach is applicable for stochastic subdiffusion equation.</p>