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A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations. (English) Zbl 0765.65069

The numerical solution of the initial value problem for delay- differential equations \(x'(t)=f(t,x(t),x(t-\tau))\), \(t\geq 0\), \(x(t)=g(t)\), \(t\leq 0\) is considered. A new interpolation procedure is introduced which leads to numerical processes that satisfy an asymptotic stability condition related to the class of test problems \(x'(t)=\lambda x(t)+\mu x(t-\tau)\) with \(\lambda\) and \(\mu\in\mathbb{C}\), \(\text{Re}(\lambda)<-|\mu|\) and \(\tau>0\).

MSC:

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

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