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 attr...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.展开更多
By employing the improved moving least-square(EVILS) approximation,the improved element-free Galerkin(IEFG)method is presented for the unsteady Schr?dinger equation.In the E3 FG method,the two-dimensional(2D) trial fu...By employing the improved moving least-square(EVILS) approximation,the improved element-free Galerkin(IEFG)method is presented for the unsteady Schr?dinger equation.In the E3 FG method,the two-dimensional(2D) trial function is approximated by the IMLS approximation,the variation method is used to obtain the discrete equations,and the essential boundary conditions are imposed by the penalty method.Because the number of coefficients in the IMLS approximation is less than in the moving least-square(MLS) approximation,fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted.Then the IEFG method has high computational efficiency and accuracy.Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.展开更多
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 o...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.展开更多
The present paper deals with the numerical solution of a two-dimensional linear hyperbolic equation by using the element-free Galerkin (EFG) method which is based on the moving least-square approximation for the test ...The present paper deals with the numerical solution of a two-dimensional linear hyperbolic equation by using the element-free Galerkin (EFG) method which is based on the moving least-square approximation for the test and trial functions. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for hyperbolic problems needs only the scattered nodes instead of meshing the domain of the problem. It neither requires any element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for two-dimensional hyperbolic problems is investigated by two numerical examples in this paper.展开更多
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 e...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.展开更多
In this paper,we analyze the generalized Camassa and Holm(CH) equation by the improved element-free Galerkin(IEFG) method.By employing the improved moving least-square(IMLS) approximation,we derive the formulas for th...In this paper,we analyze the generalized Camassa and Holm(CH) equation by the improved element-free Galerkin(IEFG) method.By employing the improved moving least-square(IMLS) approximation,we derive the formulas for the generalized CH equation with the IEFG method.A variational method is used to obtain the discrete equations,and the essential boundary conditions are enforced by the penalty method.Because there are fewer coefficients in the IMLS approximation than in the MLS approximation,and in the IEFG method,fewer nodes are selected in the entire domain than in the conventional EFG method,the IEFG method should result in a higher computing speed.The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.展开更多
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 fie...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.展开更多
The element-free Galerkin (EFG) method is used in this paper to find the numerical solution to a regularized long-wave (RLW) equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essent...The element-free Galerkin (EFG) method is used in this paper to find the numerical solution to a regularized long-wave (RLW) equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. The effectiveness of the EFG method of solving the RLW equation is investigated by two numerical examples in this paper.展开更多
The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion eq...The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion equation was solved. Under suitable conditions, the formal asymptotic solutions were constructed using the method of two-step expansions and the uniform validity of the solutions was proved using the differential inequality.展开更多
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 movin...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 interpolation 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.展开更多
基金supported by the Natural Science Foundation of Ningbo,China (Grant Nos.2009A610014 and 2009A610154)the Natural Science Foundation of Zhejiang Province,China (Grant No.Y6090131)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171208)the Natural Science Foundation of Zhejiang Province,China(Grant No.LY15A020007)+1 种基金the Natural Science Foundation of Ningbo City(Grant No.2014A610028)the K.C.Wong Magna Fund in Ningbo University,China
文摘By employing the improved moving least-square(EVILS) approximation,the improved element-free Galerkin(IEFG)method is presented for the unsteady Schr?dinger equation.In the E3 FG method,the two-dimensional(2D) trial function is approximated by the IMLS approximation,the variation method is used to obtain the discrete equations,and the essential boundary conditions are imposed by the penalty method.Because the number of coefficients in the IMLS approximation is less than in the moving least-square(MLS) approximation,fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted.Then the IEFG method has high computational efficiency and accuracy.Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11372166,11372147,61074142,and 11072117)the Scientific Research Fund of Zhejiang Province,China(Grant No.LY13A010005)+1 种基金the Disciplinary Project of Ningbo City,China(Grant No.SZXL1067)the K.C.Wong Magna Fund in Ningbo University,China,and the Government of the Hong Kong Administrative Region,China(Grant No.119011)
文摘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.
基金Project supported by the Natural Science Foundation of Ningbo, China (Grant Nos 2009A610014, 2009A610154, 2008A610020 and 2007A610050)
文摘The present paper deals with the numerical solution of a two-dimensional linear hyperbolic equation by using the element-free Galerkin (EFG) method which is based on the moving least-square approximation for the test and trial functions. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for hyperbolic problems needs only the scattered nodes instead of meshing the domain of the problem. It neither requires any element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for two-dimensional hyperbolic problems is investigated by two numerical examples in this paper.
基金Project supported by the National Natural Science Foundation of China (Grant No.10871124)the Natural Science Foundation of Zhejiang Province of China (Grant No.Y6110007)
文摘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.
基金supported by the Natural Science Foundation of Ningbo City,Zhejiang Province,China (Grant Nos. 2012A610038 and 2012A610023)the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6110007)
文摘In this paper,we analyze the generalized Camassa and Holm(CH) equation by the improved element-free Galerkin(IEFG) method.By employing the improved moving least-square(IMLS) approximation,we derive the formulas for the generalized CH equation with the IEFG method.A variational method is used to obtain the discrete equations,and the essential boundary conditions are enforced by the penalty method.Because there are fewer coefficients in the IMLS approximation than in the MLS approximation,and in the IEFG method,fewer nodes are selected in the entire domain than in the conventional EFG method,the IEFG method should result in a higher computing speed.The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6110007)
文摘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.
基金supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6110007)
文摘The element-free Galerkin (EFG) method is used in this paper to find the numerical solution to a regularized long-wave (RLW) equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. The effectiveness of the EFG method of solving the RLW equation is investigated by two numerical examples in this paper.
基金Project supported by National Natural Science Foundation ofChina(Grant No .10071048)
文摘The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion equation was solved. Under suitable conditions, the formal asymptotic solutions were constructed using the method of two-step expansions and the uniform validity of the solutions was proved using the differential inequality.
基金Project supported by the National Natural Science Foundation of China(Grant No.11072117)the Natural Science Foundation of Ningbo City,China(GrantNo.2013A610103)+2 种基金the Natural Science Foundation of Zhejiang Province,China(Grant No.Y6090131)the Disciplinary Project of Ningbo City,China(GrantNo.SZXL1067)the K.C.Wong Magna Fund in Ningbo University,China
文摘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 interpolation 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.
