On the numerical stability of the general linear methods for Volterra integro-differential equations

摘要

This paper deals with the stability analysis of the methods for Volterra integro-differential equations based on the convolution test equation. These methods are designed by the combination of diagonally implicit multistage integration methods of types 1 and 2 with Gregory quadrature rule. Some theoretical results are achieved by providing corresponding recurrence relation and stability matrix. The obtained theoretical results are verified by some numerical experiments. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.