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Nonlinear stability of Runge-Kutta methods for neutral delay integro-differential equations. (English) Zbl 1193.65123
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:
 65L06 Multistep, Runge-Kutta, and extrapolation methods 34K28 Numerical approximation of solutions of functional-differential equations 34K40 Neutral functional-differential equations
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References:
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