𝔖 Bobbio Scriptorium
✦   LIBER   ✦

IMEX Runge–Kutta schemes for reaction–diffusion equations

✍ Scribed by Toshiyuki Koto

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
703 KB
Volume
215
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

A fundamental research is carried out into convergence and stability properties of IMEX (implicit-explicit) Runge-Kutta schemes applied to reaction-diffusion equations. It is shown that a fully discrete scheme converges if it satisfies certain conditions using a technique of the B-convergence analysis, developed by Burrage, Hundsdorfer and Verwer in 1986. Stability of the schemes is also examined on the basis of a scalar test equation, proposed by Frank, Hundsdorfer and Verwer in 1997.

📜 SIMILAR VOLUMES

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

Multirate Runge–Kutta schemes for advect
Multirate Runge–Kutta schemes for advection equations
✍ Martin Schlegel; Oswald Knoth; Martin Arnold; Ralf Wolke 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 905 KB

a b s t r a c t Explicit time integration methods can be employed to simulate a broad spectrum of physical phenomena. The wide range of scales encountered lead to the problem that the fastest cell of the simulation dictates the global time step. Multirate time integration methods can be employed to

Stability and convergence of staggered R
Stability and convergence of staggered Runge–Kutta schemes for semilinear wave equations
✍ Daisuke Murai; Toshiyuki Koto 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 294 KB

A staggered Runge-Kutta (staggered RK) scheme is a Runge-Kutta type scheme using a time staggered grid, as proposed by Ghrist et al. in 2000 [6]. Afterwards, Verwer in two papers investigated the efficiency of a scheme proposed by Ghrist et al. [6] for linear wave equations. We study stability and c