Nonlinear stability and asymptotic stability of implicit Euler method for stiff Volterra functional differential equations in Banach spaces

This paper is concerned with the numerical solution of Volterra functional differential equations. We focus on the stability and asymptotic stability properties of implicit Euler method when applied to nonlinear stiff Volterra functional differential equations in Banach spaces. A series of new stability and asymptotic stability results are obtained. Numerical example is given to confirm the theoretical results.