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Zbl 1193.65123
Yu, Yuexin; Wen, Liping; Li, Shoufu
Nonlinear stability of Runge-Kutta methods for neutral delay integro-differential equations. (English)
[J] Appl. Math. Comput. 191, No. 2, 543-549 (2007). ISSN 0096-3003

Summary: The present paper is concerned with the numerical solution to initial value problems of neutral delay integro-differential equations (NDIDEs). The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for a class $R(\alpha ,\beta _{1},\beta _{2},\gamma )$ of nonlinear systems of NDIDEs are derived. A numerical test that confirms the theoretical results is given in the end.

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
34K28 Numerical approximation of solutions of FDE
34K40 Neutral equations

Keywords: neutral delay integro-differential equations; Runge-Kutta methods; stability; asymptotic stability

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Zentralblatt MATH Berlin [Germany]