On a new class of BDF and IMEX schemes for parabolic type equations
arxiv(2024)
摘要
When applying the classical multistep schemes for solving differential
equations, one often faces the dilemma that smaller time steps are needed with
higher-order schemes, making it impractical to use high-order schemes for stiff
problems. We construct in this paper a new class of BDF and implicit-explicit
(IMEX) schemes for parabolic type equations based on the Taylor expansions at
time t^n+β with β > 1 being a tunable parameter. These new
schemes, with a suitable β, allow larger time steps at higher-order for
stiff problems than that is allowed with a usual higher-order scheme. For
parabolic type equations, we identify an explicit uniform multiplier for the
new second- to fourth-order schemes, and conduct rigorously stability and error
analysis by using the energy argument. We also present ample numerical examples
to validate our findings.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要