This paper deals with convergence and stability of exponential Runge-Kutta methods of collocation type for delay differential equations. It is proved that these kinds of numerical methods converge at least with their stage order. Moreover, a sufficient condition of the numerical stability is provide
Interpolating Runge-Kutta methods for vanishing delay differential equations
β Scribed by W. H. Enright; M. Hu
- Publisher
- Springer Vienna
- Year
- 1995
- Tongue
- English
- Weight
- 669 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0010-485X
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π SIMILAR VOLUMES
Stability of IMEX (implicit-explicit) Runge-Kutta methods applied to delay differential equations (DDEs) is studied on the basis of the scalar test equation du/dt = u(t) + u(t -), where is a constant delay and , are complex parameters. More specifically, P-stability regions of the methods are define
In this paper the author investigates the stability of numerical methods for general delay differential equations of the type { y'(t) = j(t, y(t), y(a(t))), t 2 to, where a(t) < t and y(t) is a vector complex-valued function. Contractivity conditions are found for Runge-Kutta methods as applied to
A sufficient condition of stability of exponential Runge-Kutta methods for delay differential equations is obtained. Furthermore, a relationship between P-stability and GP-stability is established. It is proved that the numerical methods can preserve the analytical stability for a class of test prob