On a new class of BDF and IMEX schemes for parabolic type equations
<|reference_start|>On a new class of BDF and IMEX schemes for parabolic type equations: 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 $t^{n+\beta}$ with $\beta > 1$ being a tunable parameter. These new schemes, with a suitable $\beta$, 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.<|reference_end|>
@article{huang2024on,
    title={On a new class of BDF and IMEX schemes for parabolic type equations},
    author={Fukeng Huang and Jie Shen},
    journal={arXiv preprint arXiv:2405.00300},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.00300},
    primaryClass={math.NA cs.NA}
}