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
Construction of highly stable parallel two-step Runge–Kutta methods for delay differential equations
✍ Scribed by Z. Bartoszewski; Z. Jackiewicz
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 471 KB
- Volume
- 220
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
It is shown that any A-stable two-step Runge-Kutta method of order p and stage order q = p for ordinary differential equations can be extended to the P-stable method of uniform order p = p for delay differential equations.
📜 SIMILAR VOLUMES
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
This paper deals with stability properties of Runge-Kutta methods for the initial value problem in nonlinear neutral delay differential equations The new concepts of GS(l)-stability, GAS(l)-stability and Weak GAS(l)-stability are introduced, and it is shown that (k, l)algebraically stable Runge-Kut