A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
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DOI：
10.1007/bf01994847
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发表时间：
1992-12
影响因子：
1.5
通讯作者：
K. I. Hout
中科院分区：
文献类型：
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作者：
K. I. Hout
本文讨论了用龙格-库塔法求解滞后微分方程的问题。引入了一种新的插值方法，使得数值过程满足与一类检验问题U ′（t）=λU（t）+μU（t-τ）相关的重要渐近稳定性条件，其中λ，μ ε C，Re（λ）<-|μ|，且τ>0。如果fci表示给定龙格库塔方法的第i个横坐标，则在第n-1→tn：=tn-1+霍夫的数值过程的第n步中，我们的插值过程从已经由该过程在点stj-1+cih（j= 1，2，3，.）生成的近似计算U（tn-1+cih-τ）的近似。对于其中两个新过程和一个标准过程，我们将考虑在实际应用中对给定的刚性问题的收敛行为。
This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU′(t)=λU(t)+μU(t−τ) with λ, μ ε C, Re(λ)<−|μ|, and τ>0. Ifcidenotes theith abscissa of a given Runge-Kutta method, then in thenth steptn−1→tn:=tn−1+hof the numerical process our interpolation procedure computes an approximation toU(tn−1+cih−τ) from approximations that have already been generated by the process at pointstj−1+cih(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem.