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Stability of some continuously imbedded Runge-Kutta methods of Sarafyan

✍ Scribed by S. Thompson

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
202 KB
Volume
13
Category
Article
ISSN
0898-1221

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✦ Synopsis

Sarafyan and others have recently developed novel explicit Runge-Kutta methods. Associated with each method is an imbedded polynomial which interpolates the Runge-Kutta method and which is itself a Runge-Kutta approximation at non-meshpoints. In this paper, we show that the interpolation polynomials possess the desirable stability properties of the Runge-Kutta methods.

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✍ Toshiyuki Koto 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 353 KB

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