Nonlinear Stability and D‐Convergence of Additive Runge‐Kutta Methods for Multidelay‐Integro‐Differential Equations

Haiyan Yuan, Jingjun Zhao and Yang Xu

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: This paper is devoted to the stability and convergence analysis of the Additive Runge‐Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of multidelay‐integro‐differential equations (MDIDEs). GDN‐stability and D‐convergence are introduced and proved. It is shown that strongly algebraically stability gives D‐convergence, DA‐ DAS‐ and ASI‐stability give GDN‐stability. A numerical example is given to illustrate the theoretical results.

Date: 2012
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https://doi.org/10.1155/2012/854517

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:854517

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