Stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations

This paper deals with stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations (FIDEs). A type of extended one-leg methods are suggested for the FIDEs. The (weak) global stability results of the methods are presented. In particular, it is shown under suitable condition that a G-stable extended BDF method is globally and asymptotically stable for the problems of class FID(α,β,γ,η,+∞)FID(α,β,γ,η,+∞). Numerical experiments further illustrate the theoretical results and the methodical effectiveness. In the end, a connection and comparison between the obtained results and the existed ones is given.