论文标题
具有单一源术语的细节模型的修改BDF2方案
Modified BDF2 schemes for subdiffusion models with a singular source term
论文作者
论文摘要
本文的目的是研究用弱奇异源项近乎求解次扩散方程的时间阶梯方案。在这种情况下，许多流行的时间步进方案，包括校正高阶BDF方法，可能会失去其高阶精度。为了填补这一差距，在本文中，我们开发了一种新颖的时间步进方案，其中源项是通过使用$ k $折叠的积分衍生词正规化的，并且通过使用修改的BDF2卷积正交正常来离散方程。我们证明，即使源术语在时间上不平整并且与初始数据不兼容，我们提出的时间步进方案是二阶的。提出数值结果以支持理论结果。
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.
