A meshless method for the compound KdV-Burgers equation

The element-free Galerkin (EFG) method for numerically solving the compound Korteweg-de Vries-Burgers (KdVB) equation is discussed in this paper.The Galerkin weak form is used to obtain the discrete equation and the essential boundary conditions are enforced by the penalty method.The effectiveness of the EFG method of solving the compound Korteweg-de Vries-Burgers (KdVB) equation is illustrated by three numerical examples.     

An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)

A generalized Fisher equation(GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance.The exact mathematical result of the GFE has been widely used in population dynamics and genetics,where it originated.Many researchers have studied the numerical solutions of the GFE,up to now.In this paper,we introduce an element-free Galerkin(EFG) method based on the moving least-square approximation to approximate positive solutions of the GFE from population dynamics.Compared with other numerical methods,the EFG method for the GFE needs only scattered nodes instead of meshing the domain of the problem.The Galerkin weak form is used to obtain the discrete equations,and the essential boundary conditions are enforced by the penalty method.In comparison with the traditional method,numerical solutions show that the new method has higher accuracy and better convergence.Several numerical examples are presented to demonstrate the effectiveness of the method.     

An element-free Galerkin(EFG) method for numerical solution of the coupled Schrdinger-KdV equations

The present paper deals with the numerical solution of the coupled Schrdinger-KdV equations using the elementfree Galerkin(EFG) method which is based on the moving least-square approximation.Instead of traditional mesh oriented methods such as the finite difference method(FDM) and the finite element method(FEM),this method needs only scattered nodes in the domain.For this scheme,a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method.In numerical experiments,the results are presented and compared with the findings of the finite element method,the radial basis functions method,and an analytical solution to confirm the good accuracy of the presented scheme.     

飞秒脉冲激光对纳米金属薄膜传导模型的解

研究了一类飞秒脉冲激光对纳米金属薄膜传导模型. 首先求出模型的退化解, 然后利用摄动理论和方法, 得到了相应模型的任意次渐近解. 最后论述了解的渐近性态. 关键词： 飞秒脉冲 激光 渐近性态     

Analysis of the equal width wave equation with the mesh-free reproducing kernel particle Ritz method

In this paper,we analyse the equal width(EW) wave equation by using the mesh-free reproducing kernel particle Ritz(kp-Ritz) method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.     

Meshless analysis of three-dimensional steady-state heat conduction problems

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson’s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.     

Element-free Galerkin method for a kind of KdV equation

The present paper deals with the numerical solution of the third-order nonlinear KdV equation using the element-free Galerkin (EFG) method which is based on the moving least-squares approximation. A variational method is used to obtain discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for KdV equations needs only scattered nodes instead of meshing the domain of the problem. It does not require any element connectivity and does not suffer much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for the KdV equation is investigated by two numerical examples in this paper.     

具有控制项的弱非线性发展方程行波解

利用解析方法研究了一类具有控制项的弱非线性发展方程. 由摄动理论得到了相应方程的渐近解,并研究了控制项对渐近解的影响. 关键词： 发展方程 扰动 控制函数     

A control method applied to mixed traffic flow for the coupled-map car-following model

In light of previous work [Phys. Rev. E 60 4000 （1999）], a modified coupled-map car-following model is proposed by considering the headways of two successive vehicles in front of a considered vehicle described by the optimal velocity function. The non-jam conditions are given on the basis of control theory. Through simulation, we find that our model can exhibit a better effect as p = 0.65, which is a parameter in the optimal velocity function. The control scheme, which was proposed by Zhao and Gao, is introduced into the modified model and the feedback gain range is determined. In addition, a modified control method is applied to a mixed traffic system that consists of two types of vehicle. The range of gains is also obtained by theoretical analysis. Comparisons between our method and that of Zhao and Gao are carried out, and the corresponding numerical simulation results demonstrate that the temporal behavior of traffic flow obtained using our method is better than that proposed by Zhao and Gao in mixed traffic systems.     

A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging inter- polation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.