A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
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 \(\tau>0\).
scientific article; zbMATH DE number 86147
scientific article