Explicit general linear methods with a large stability region for Volterra integro-differential equations

Abstract

In this paper, we describe the construction of a class of methods with a large area of the stability region for solving Volterra integro-differential equations. In the structure of these methods which is based on a subclass of explicit general linear methods with and without Runge-Kutta stability property, we use an adequate quadrature rule to approximate the integral term of the equation. The free parameters of the methods are used to obtain methods with a large stability region. The efficiency of the proposed methods is verified with some numerical experiments and comparisons with other existing methods.

Keywords

• Volterra integro-differential equations
• general linear methods
• Runge–Kutta stability
• region of absolute stability
• Gregory quadrature rule