نتایج جستجو برای: runge

تعداد نتایج: 4473  

Journal: :Math. Comput. 1998
Sigal Gottlieb Chi-Wang Shu

In this paper we further explore a class of high order TVD (total variation diminishing) Runge-Kutta time discretization initialized in a paper by Shu and Osher, suitable for solving hyperbolic conservation laws with stable spatial discretizations. We illustrate with numerical examples that non-TVD but linearly stable Runge-Kutta time discretization can generate oscillations even for TVD (total...

Journal: :Numerische Mathematik 2009
Jialin Hong Shanshan Jiang Chun Li

We investigate conservative properties of Runge-Kutta methods for Hamiltonian PDEs. It is shown that multi-symplecitic Runge-Kutta methods preserve precisely norm square conservation law. Based on the study of accuracy of Runge-Kutta methods applied to ordinary and partial differential equations, we present some results on the numerical accuracy of conservation laws of energy and momentum for H...

2013
Pieter D. Boom David. W. Zingg

This paper presents an overview of high-order implicit time integration methods and their associated properties with a specific focus on their application to computational fluid dynamics. A framework is constructed for the development and optimization of general implicit time integration methods, specifically including linear multistep, Runge-Kutta, and multistep Runge-Kutta methods. The analys...

Journal: :Archives of Women's Mental Health 2016

Journal: :Math. Comput. 2000
Shoufu Li

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 ...

Journal: :Archiv für Gynäkologie 1909

Journal: :iranian journal of numerical analysis and optimization 0

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...

2004
CHENGJIAN ZHANG STEFAN VANDEWALLE

This paper deals with the stability of Runge–Kutta methods for a class of stiff systems of nonlinear Volterra delay-integro-differential equations. Two classes of methods are considered: Runge–Kutta methods extended with a compound quadrature rule, and Runge– Kutta methods extended with a Pouzet type quadrature technique. Global and asymptotic stability criteria for both types of methods are de...

2001
Hiroshi Sugiura Tatsuo Torii

Sugiura, H. and T. Torii, A method for constructing generalized Runge-Kutta methods, Journal of Computational and Applied Mathematics 38 (1991) 399-410. In the implementation of an implicit Runge-Kutta formula, we need to solve systems of nonlinear equations. In this paper, we analyze the Newton iteration process and a modified Newton iteration process for solving these equations. Then we propo...

Journal: :Numerische Mathematik 2011
Lehel Banjai Christian Lubich Jens Markus Melenk

An error analysis of Runge-Kutta convolution quadrature is presented for a class of nonsectorial operators whose Laplace transform satisfies, besides the standard assumptions of analyticity in a half-plane Re s > σ0 and a polynomial bound O(s 1) there, the stronger polynomial bound O(s2) in convex sectors of the form | arg s| ≤ π/2 − θ < π/2 for θ > 0. The order of convergence of the Runge-Kutt...

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