Frontiers of Mathematics in China vol:4 issue:1 pages:63-87
This paper is concerned with the study of the stability of Runge-Kutta-Pouzet methods for Volterra integro-di®erential equations with delays. We are interested in the comparison between analytical and numerical stability regions. First, we focus on scalar equations with real coe±cients. It is
proved that all Gauss-Pouzet methods can retain the asymptotic stability of the analytical solution. Then, we consider multidimensional case. A new stability condition for the stability of the analytical solution is given. Under this condition, the asymptotic stability of Gauss-Pouzet methods is investigated.