The numerical stability of multistep methods for Volterra integral equations with many delays

Abstract

This paper deals with the stability analysis of modified multilag (MML) methods for numerical solution of Volterra integral equations with many constant delays. We focus on the stability behaviour of such methods when they are applied to the following equation.

where p, q_j  ∈ C, j = 1, 2, …, r, d_r  ≥ d_{r −1} ≥ ··· ≥ d ₁ > 0, and ψ(x) is a specified initial function. We investigate the stability properties of MML methods in the case of earlier equation.

Keywords:

• Modified multilag method
• Volterra integral equations
• Delay
• P(δ1, …, δr)-stable
• GPr-stable

Acknowledgement

I would like to thank Professor S. El-Gendi, Dr. A. B. Shamardan, Assiut University and Dr. A. El-Safty, Department of Mathematics, Qatar University for helpful discussions.