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arXiv · 2305.06571

Numerical Stability for Differential Equations with Memory

Guihong Wang·Yuqing Li·Tao Luo·Zheng Ma·Nung Kwan Yip·Guang Lin
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Abstract

In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some sufficient conditions for the stability and convergence of some common multi-step methods, and accordingly, a notion of A-stability for differential equations with memory. Finally, we carry out the computational performance of our theory through numerical examples.

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Guihong Wang, Yuqing Li, Tao Luo, Zheng Ma, Nung Kwan Yip, Guang Lin. 2023-10-27. Numerical Stability for Differential Equations with Memory. https://arxiv.org/abs/2305.06571

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