Stability analysis of implicit–explicit [formula omitted]-methods for composite stiff neutral functional differential equations in Banach space

Abstract

This paper is concerned with the stability and asymptotic stability of implicit–explicit (IMEX) θ-methods for composite stiff neutral functional differential equations in Banach space. The stability and asymptotic stability conditions of the methods are obtained. The given numerical experiments confirmed the accuracy of the obtained theoretical results and showed that the IMEX θ-methods have a higher computational efficiency compared to the θ-methods in the end.