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

    Hassan Mahdi Affiliation
    ; Gholamreza Hojjati Affiliation
    ; Ali Abdi Affiliation

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.

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

How to Cite
Mahdi, H., Hojjati, G., & Abdi, A. (2019). Explicit general linear methods with a large stability region for Volterra integro-differential equations. Mathematical Modelling and Analysis, 24(4), 478-493. https://doi.org/10.3846/mma.2019.029
Published in Issue
Oct 25, 2019
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