Numerical Stability for Differential Equations with Memory

2023/05/11 by Wang, Guihong, Li, Yuqing, Luo, Tao +3
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2305.06571

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.

Related

• Linear Multistep Numerical Methods for Ordinary Differential Equations
• A multistep algorithm for ODEs
• Stability and bifurcation properties of the algorithms for keeping of differential equations solutions on the required level
• Minimal residual multistep methods for large stiff non-autonomous linear problems
• High order semi-implicit multistep methods for time dependent partial\n differential equations