We investigate stability properties of two-step Runge-Kutta methods with respect to the linear test equation y'(t) = ay(t) + by(t -T), t > O, where a and b are complex parameters. It is known that the solution y(t) to this equation tends to zero as t --~ oc if Ibl < -Re(a). We will show that under
GP-Stability of two-step implicit runge-kutta methods for delay differential equations
β Scribed by Yang, Biao; Esaki, Nobuyuki; Mitsui, Taketomo
- Book ID
- 119953213
- Publisher
- Taylor and Francis Group
- Year
- 2000
- Tongue
- English
- Weight
- 298 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0020-7160
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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
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