## 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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