New Interpolation Procedure for Adapting Runge-Kutta Methods to Delay Differential Equations

摘要

The 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 stability condition with respect to the test equation U'(t)=(lambda)U(t)+(mu)U(t-tau) where (lambda), (mu)(epsilon)C, Re(lambda)0. A numerical illustration is given for two of these new processes, in comparison to a standard process.