B-Convergence Properties of Multistep Runge-Kutta Methods
نویسندگان
چکیده
منابع مشابه
Stability and B-convergence properties of multistep Runge-Kutta methods
This paper continues earlier work by the same author concerning the stability and B-convergence properties of multistep Runge-Kutta methods for the numerical solution of nonlinear stiff initial-value problems in a Hilbert space. A series of sufficient conditions and necessary conditions for a multistep Runge-Kutta method to be algebraically stable, diagonally stable, Bor optimally B-convergent ...
متن کاملSome Properties of Symplectic Runge-kutta Methods
We prove that to every rational function R(z) satisfying R(−z)R(z) = 1, there exists a symplectic Runge-Kutta method with R(z) as stability function. Moreover, we give a surprising relation between the poles of R(z) and the weights of the quadrature formula associated with a symplectic Runge-Kutta method.
متن کاملEquilibrium attractive properties of a class of multistep Runge-Kutta methods
The main purpose of this paper is to discuss the equilibrium attractive properties of a class of multistep Runge–Kutta methods for initial value problems of ordinary differential equations. Some algebraic conditions insuring the equilibrium attractivity are given, and some methods satisfying these algebraic conditions are constructed. Some numerical examples confirm our results. 2005 Elsevier I...
متن کاملRunge - Kutta Methods page RK 1 Runge - Kutta Methods
Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...
متن کاملAccelerated Runge-Kutta Methods
Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step of integration, respectively. In this paper, we propose a set of simple, explicit, and constant step-size Accerelated-Runge-Kutta methods that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1994
ISSN: 0025-5718
DOI: 10.2307/2153523