نتایج جستجو برای: runge kutta method

تعداد نتایج: 1631928  

Journal: :SIAM J. Scientific Computing 2014
Robert I. McLachlan Brett N. Ryland Yajuan Sun

We study the spatial semidiscretizations obtained by applying Runge–Kutta (RK) and partitioned Runge–Kutta (PRK) methods to multisymplectic Hamiltonian partial differential equations. These methods can be regarded as multisymplectic hp-finite element methods for wave equations. All the methods we consider are multisymplectic; we determine their properties with regard to existence of solutions, ...

Journal: :J. Computational Applied Mathematics 2012
Kevin Burrage Pamela M. Burrage

In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM(s, r) methods to construct symplectic Runge-Kutta methods for all values of s and r with s ≥ r. However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which re...

2012
Elena Celledoni Robert I McLachlan Brynjulf Owren W Quispel

We show that Kahan’s discretization of quadratic vector fields is equivalent to a Runge–Kutta method. When the vector field is Hamiltonian on either a symplectic vector space or a Poisson vector space with constant Poisson structure, the map determined by this discretization has a conserved modified Hamiltonian and an invariant measure, a combination previously unknown amongst Runge–Kutta metho...

Journal: :Int. J. Comput. Math. 2007
Brett N. Ryland Robert I. McLachlan Jason Frank

Although Runge–Kutta and partitioned Runge–Kutta methods are known to formally satisfy discrete multisymplectic conservation laws when applied to multi-Hamiltonian PDEs, they do not always lead to well-defined numerical methods. We consider the case study of the nonlinear Schrödinger equation in detail, for which the previously known multisymplectic integrators are fully implicit and based on t...

Journal: :iranian journal of science and technology (sciences) 2011
m. merdan

in this paper, the approximate solution of the differential system modeling hiv infection of cd4+ t cells isobtained by a reliable algorithm based on an adaptation of the standard variational iteration method (vim), which is called the multi-stage variational iteration method(msvim). a comparison between msvim and the fourthorder runge-kutta method (rk4-method) reveal that the proposed techniqu...

2015
GEORGIOS AKRIVIS VASSILIOS A. DOUGALIS OHANNES KARAKASHIAN

We construct and analyze iterative methods for the efficient solution of the nonlinear equations that result from the application of Implicit Runge–Kutta methods to the temporal integration of nonlinear evolution equations. Some of the schemes we consider have as starting point Newton’s method and can be applied to a large class of evolution equations. RÈSUMÈ. On construit et analyse des méthod...

2012

This study utilized combination of phase plots,time steps distribution and adaptive time steps Runge-Kutta and f if th order algorithms to investigate a harmonically Duff ing oscillator.The object is to visually compare fourth and f if th order Runge-Kutta algorithms performance as tools for seeking the chaotic solutions of a harmonically excited Duffing oscillator.Though fif th order algorithm...

2015
Mukaddes ÖKTEN TURACI Turgut ÖZİŞ

Recently, the Runge-Kutta methods, obtained via Taylor’s expansion is exist in the literature. In this study, we have derived explicit methods for problems of the form y′ = f(y) including second and third derivatives , by considering available Two-Derivative Runge-Kutta methods (TDRK). The methods use one evaluation of first derivative, one evaluation of second derivative and many evaluations o...

Journal: :caspian journal of mathematical sciences 2014
b. pourhassan j. khalilzadeh

in this paper, we consider non-linear ginsburg-pitaevski-gross equation with the rosen-morse and modifiedwoods-saxon potentials which is corresponding to the quantum vortices and has important applications in turbulence theory. we use the runge- kutta-fehlberg approximation method to solve the resulting non-linear equation.

Journal: :J. Applied Mathematics 2012
Rohana Abdul Hamid Wan Mohd Khairy Adly Wan Zaimi Norihan M. Arifin Nor Ashikin Abu Bakar Biliana Bidin

The problem of thermal diffusion and diffusion thermo effects on thermosolutal Marangoni convection flow of an electrically conducting fluid over a permeable surface is investigated. Using appropriate similarity transformations, the governing system of partial differential equation is transformed to a set of nonlinear ordinary differential equations, then solved numerically using the Runge-Kutt...

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