Summary.
This paper investigates the stability of Runge-Kutta methods when they are applied to the complex linear scalar delay differential equation \(y^{\prime }\left( t\right) =ay\left(t\right) +by\left( t-1\right) \). This kind of stability is called \(\tau -\)stability. We give a characterization of \(\tau -\) stable Runge-Kutta methods and then we prove that implicit Euler method is \(\tau -\)stable.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received November 3, 1998 / Revised version received March 23, 1999 / Published online July 12, 2000
Rights and permissions
About this article
Cite this article
Maset, S. Stability of Runge-Kutta methods for linear delay differential equations. Numer. Math. 87, 355–371 (2000). https://doi.org/10.1007/s002110000179
Issue Date:
DOI: https://doi.org/10.1007/s002110000179