Numerical Stability for Differential Equations with Memory

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

Published 2023-05-11Version 1

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.