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Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations. (English) Zbl 0904.65082

Stability and convergence of Runge-Kutta methods with Lagrangian interpolation applied to nonlinear ordinary delay differential equations are studied. The new concepts of strong algebraic stability, GDN-stability and D-convergence are introduced to facilitate the analysis. A correspondence between certain stability properties of Runge-Kutta methods applied to ordinary differential equations and relevant stability properties of the same methods enhanced by Lagrangian interpolation and applied to delay differential equations is established.

MSC:

65L20 Stability and convergence of numerical methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34K05 General theory of functional-differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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