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

摘要

This paper is concerned with the dissipativity of a class of nonlinear functional-integro-differential equations (FIDEs). The dissipativity result of the theoretical solution for this class problem is presented. A type of extended one-leg methods is suggested for the FIDEs. It is shown under suitable condition that a G(c,p,0)-algebraically stable one-leg method is dissipative when applied to the above problem. Numerical examples are given to illustrate the correctness of our theoretical results.