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Zbl 1057.65104
Zhang, Chengjian; Vandewalle, Stefan
Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. (English)
[J] IMA J. Numer. Anal. 24, No. 2, 193-214 (2004). ISSN 0272-4979; ISSN 1464-3642/e

The authors study stiff and nonlinear Volterra delay-integro-differential equations (VDIDE). A discretization is done by using Runge-Kutta methods for which the stability is studied. Two classes of discretization schemes are considered and their stability properties are discussed. Then global and asymptotic stability criteria for the two classes of methods are derived. A Pouzet type quadrature technique is used. Applications to some classical Runge-Kutta schemes are given, for instance those of Gauss, Radau or Labatto type. This work is based on algebraic stability which generally does not bring on an order barrier.
[Yves Cherruault (Paris)]

MSC 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations

Keywords: quadrature method; nonlinear Volterra delay-integro-differential equations; Runge-Kutta methods; asymptotic stability; algebraic stability

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