In this paper, we apply the higher order self-adjoint schemes constructed in [1] to wave equation and heat equation to show these methods can also be used to solve partial differential equations to get higher order ac...
In this paper, we apply the higher order self-adjoint schemes constructed in [1] to wave equation and heat equation to show these methods can also be used to solve partial differential equations to get higher order accuracy in the time direction.
In this paper, we discuss the conditions for Euler midpoint rule to be volume-preserving and present explicit volume preserving schemes. Some numerical experiments are done to test these schemes.
In this paper, we discuss the conditions for Euler midpoint rule to be volume-preserving and present explicit volume preserving schemes. Some numerical experiments are done to test these schemes.
In this paper, we discuss the conditions for the Euler midpoint rule to be volume-preserving and present Euler type explicit volume-preserving schemes. Some numerical applications to the system defining rigid body mot...
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In this paper, we discuss the conditions for the Euler midpoint rule to be volume-preserving and present Euler type explicit volume-preserving schemes. Some numerical applications to the system defining rigid body motion and the ABC flow are also given.
We use formal power series to expand the method used by Yoshida in constructing explicit canonical higher order schemes for separable Hamiltonian systems and construct general higher order schemes for general dynamica...
We use formal power series to expand the method used by Yoshida in constructing explicit canonical higher order schemes for separable Hamiltonian systems and construct general higher order schemes for general dynamical systems.
The stability of a three-stage difference scheme constructed in [1] is discussed, with the construction process given out concisely at first. We also present some numerical examples to test our theoretical results.
The stability of a three-stage difference scheme constructed in [1] is discussed, with the construction process given out concisely at first. We also present some numerical examples to test our theoretical results.
The main purpose of this paper is to develop and simplify the general conditions for an s-stage explicit canonical difference scheme to be of qth order while the simplified order conditions for canonical RKN methods, ...
Hamiltonian systems are canonical systems on phase space endowed with symplectic structures. The dynamical evolutions, i.e., the phase flow of the Hamiltonian systems are symplectic transformations which are area-pres...
Hamiltonian systems are canonical systems on phase space endowed with symplectic structures. The dynamical evolutions, i.e., the phase flow of the Hamiltonian systems are symplectic transformations which are area-preserving. The importance of the Hamiltonian systems and their special property require the numerical algorithms for them should preserve as much as possible the relevant symplectic properties of the original systems. Feng Kang [1-3] proposed in 1984 a new approach to computing Hamiltonian systems from the view point of symplectic geometry. He systematically described the general method for constructing symplectic schemes with any order accuracy via generating functions. A generalization of the above theory and methods for canonical Hamiltonian equations in infinite dimension can be found in [4]. Using self-adjoint schemes, we can construct schemes of arbitrary even order [5]. These schemes can be applied to wave equation [6,7] and the stability of them can be seen in [7,8]. In this paper, we will use the hyperbolic functions sinh(x), cosh(x) and tanh(x) to construct symplectic schemes of arbitrary order for wave equations and stabilities of these constructed schemes are also discussed.
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