Discrete-time waveform relaxation Volterra-Runge-Kutta methods: Convergence analysis
نویسندگان
چکیده
منابع مشابه
Discrete Hopf bifurcation for Runge-Kutta methods
Keywords: Bifurcation problems Hopf bifurcation Computational methods for bifurcation problems Attractors and their bifurcations a b s t r a c t An investigation into how well real bifurcations in the family of dynamical systems are approximated as the step-size varies is carried out. The preservation of bifurcation structures and stability under numerical simulations is discussed. In addition,...
متن کاملNonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations
and Applied Analysis 3 The class of Runge-Kutta methods with CQ formula has been applied to delay-integro-differential equations by many authors (c.f. [18, 19]). For the CQ formula (9), we usually adopt the repeated trapezoidal rule, the repeated Simpson’s rule, or the repeated Newton-cotes rule, and so forth, denote η = max{?̃? 0 , ?̃? 1 , . . . , ?̃? m }. It should be pointed out that the adopte...
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 کاملOptimum Runge-Kutta Methods
The optimum Runge-Kutta method of a particular order is the one whose truncation error is a minimum. Various measures of the size of the truncation error are considered. The optimum method is practically independent of the measure being used. Moreover, among methods of the same order which one might consider using the difference in size of the estimated error is not more than a factor of 2 or 3...
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: Journal of Computational and Applied Mathematics
سال: 1997
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(97)00168-4