On the Stability of Volterra–Runge–Kutta Methods

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1984 Switzerland English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 21, pages 123-135 (issn: 0036-1429, eissn: 1095-7170,

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Authors: Hairer, Ernst; Lubich, Christian;

doi: 10.1137/0721008

On the Stability of Volterra–Runge–Kutta Methods

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Abstract

This paper examines the stability properties of extended Runge-Kutta methods when applied to Volterra integral equations of the second kind of the form \[ y(x)=f(x)+\lambda \int^{x}_{0}k(x-s)y(s)ds\quad(x\geq 0) \] where \(Re(\lambda)0\), \(k_ 0(x)=\overline{k_ 0(-x)}\), \(x\leq 0\) there is no such order barrier.

Country

Switzerland

Related Organizations

University of Geneva
Switzerland

Keywords

extended Runge-Kutta methods, Volterra integral equations, test equations, integral equations of the second kind, algebraic stability, Numerical methods for integral equations, linear convolution equations, 510

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