نتایج جستجو برای: fourth order exponential time differenceing runge kutta method

تعداد نتایج: 3828676  

Journal: :SIAM J. Scientific Computing 2017
Ashish Bhatt Brian E. Moore

Exponential Runge-Kutta (ERK) and partitioned exponential Runge-Kutta (PERK) 4 methods are developed for solving initial value problems with vector fields that can be split into con5 servative and linear non-conservative parts. The focus is on linearly damped ordinary differential 6 equations, that possess certain invariants when the damping coefficient is zero, but, in the presence of 7 consta...

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: :Applied Mathematics and Computation 2006
Basem S. Attili Khaled M. Furati Muhammed I. Syam

We will consider the efficient implementation of a fourth order two stage implicit Runge-Kutta method to solve periodic second order initial value problems. To solve the resulting systems, we will use the factorization of the discretized operator. Such proposed factorization involves both complex and real arithmetic. The latter case is considered here. The resulting system will be efficient and...

Journal: :SIAM J. Scientific Computing 2010
Andrew J. Christlieb Colin B. Macdonald Benjamin W. Ong

In this work we discuss a class of defect correction methods which is easily adapted to create parallel time integrators for multi-core architectures and is ideally suited for developing methods which can be order adaptive in time. The method is based on Integral Deferred Correction (IDC), which was itself motivated by Spectral Deferred Correction by Dutt, Greengard and Rokhlin (BIT-2000). The ...

2012
S. Senthilkumar Abd Rahni Mt Piah

Enormous amount of real time robot arm research work is still being carried out in different aspects, especially on dynamics of robotic motion and their governing equations. Taha [5] discussed the dynamics of robot arm problems. Research in this field is still on-going and its applications are massive. This is due to its nature of extending accuracy in order to determine approximate solutions a...

2008
CHRISTIAN KLEIN

Abstract. Purely dispersive equations, such as the Korteweg-de Vries and the nonlinear Schrödinger equations in the limit of small dispersion, have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral ...

Journal: :iranian journal of science and technology (sciences) 2013
s. momani

this paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (msham). the proposed scheme is only a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. several illustrat...

2006
Christian Klein

Purely dispersive equations as the Korteweg-de Vries and the nonlinear Schrödinger equation in the limit of small dispersion have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral methods is benefic...

Journal: :J. Sci. Comput. 2007
Jan G. Verwer

Grid staggering for wave equations is a validated approach for many applications, as it generally enhances stability and accuracy. This paper is about time staggering. Our aim is to assess a fourth-order, explicit, time-staggered integration method from the literature, through a comparison with two alternative fourth-order, explicit methods. These are the classical Runge-Kutta method and a symm...

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