𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Stability analysis of two-step Runge-Kutta methods for delay differential equations

✍ Scribed by Z. Bartoszewski; Z. Jackiewicz

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
540 KB
Volume
44
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

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 some conditions this property is inherited by any A-stable two-step Runge-Kutta method applied on a constrained mesh to delay differential equations, i.e., that the corresponding method is P-stable.

📜 SIMILAR VOLUMES

Stability analysis of exponential Runge–
Stability analysis of exponential Runge–Kutta methods for delay differential equations
✍ Y. Xu; J.J. Zhao; Z.N. Sui 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 625 KB

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

Stability of IMEX Runge–Kutta methods fo
Stability of IMEX Runge–Kutta methods for delay differential equations
✍ 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

Nonlinear stability of Runge–Kutta metho
Nonlinear stability of Runge–Kutta methods for neutral delay differential equations
✍ Wan-Sheng Wang; Shou-Fu Li; Kai Su 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 277 KB

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

Exponential Runge–Kutta methods for dela
Exponential Runge–Kutta methods for delay differential equations
✍ Y. Xu; J.J. Zhao; Z.N. Sui 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 333 KB

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

New stability results for Runge–Kutta me
New stability results for Runge–Kutta methods adapted to delay differential equations
✍ Guido Van den Heuvel 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 145 KB

By using the Kreiss resolvent condition we establish upper bounds for the growth of errors in Runge-Kutta schemes for the numerical solution of delay differential equations. We consider application of such a scheme to the well-known linear test equation Z (t) = λZ(t) + µZ(tτ ), and prove that at any