共查询到18条相似文献,搜索用时 312 毫秒
1.
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. 相似文献
2.
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. 相似文献
3.
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. 相似文献
4.
In this paper, we present the local discontinuous Galerkin method for solving Burgers’ equation and the modified Burgers’ equation. We describe the algorithm formulation and practical implementation of the local discontinuous Galerkin method in detail. The method is applied to the solution of the one-dimensional viscous Burgers’ equation and two forms of the modified Burgers’ equation. The numerical results indicate that the method is very accurate and efficient. 相似文献
5.
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. 相似文献
6.
Solving coupled nonlinear Schrodinger equations via a direct discontinuous Galerkin method 下载免费PDF全文
In this work,we present the direct discontinuous Galerkin(DDG) method for the one-dimensional coupled nonlinear Schrdinger(CNLS) equation.We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system.The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge-Kutta method.Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations. 相似文献
7.
Element-free Galerkin (EFG) method for a kind of two-dimensional linear hyperbolic equation 下载免费PDF全文
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. 相似文献
8.
CHENG Xue-Ping YE Li-Jun LIN Ji 《理论物理通讯》2007,48(2):227-231
By applying Lou's direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schroedinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations. 相似文献
9.
Direct numerical simulation methods of hypersonic flat-plate boundary layer in thermally perfect gas
High-temperature effects alter the physical and transport properties of air such as vibrational excitation in a thermally perfect gas,and this factor should be considered in order to compute the flow field correctly.Herein,for the thermally perfect gas,a simple method of direct numerical simulation on flat-plat boundary layer is put forward,using the equivalent specific heat ratio instead of constant specific heat ratio in the N-S equations and flux splitting form of a calorically perfect gas.The results calculated by the new method are consistent with that by solving the N-S equations of a thermally perfect gas directly.The mean flow has the similarity,and consistent to the corresponding Blasius solution,which confirms that satisfactory results can be obtained basing on the Blasius solution as the mean flow directly in stability analysis.The amplitude growth curve of small disturbance is introduced at the inlet by using direct numerical simulation,which is consistent with that obtained by linear stability theory.It verified that the equation established and the simulation method is correct. 相似文献
10.
Pradip Roul 《理论物理通讯》2013,(9)
The purpose of the paper is to present analytical and numerical solutions of a degenerate parabolic equation with time-fractional derivatives arising in the spatial difusion of biological populations.The homotopy–perturbation method is employed for solving this class of equations,and the time-fractional derivatives are described in the sense of Caputo.Comparisons are made with those derived by Adomian’s decomposition method,revealing that the homotopy perturbation method is more accurate and convenient than the Adomian’s decomposition method.Furthermore,the results reveal that the approximate solution continuously depends on the time-fractional derivative and the proposed method incorporating the Caputo derivatives is a powerful and efcient technique for solving the fractional diferential equations without requiring linearization or restrictive assumptions.The basis ideas presented in the paper can be further applied to solve other similar fractional partial diferential equations. 相似文献
11.
An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation 下载免费PDF全文
In this paper, an improved element-free Galerkin (IEFG) method is proposed to solve the generalized fifth-order Korteweg-de Vries (gfKdV) equation. When the traditional element-free Galerkin (EFG) method is used to solve such an equation, unstable or even wrong numerical solutions may be obtained due to the violation of the consistency conditions of the moving least-squares (MLS) shape functions. To solve this problem, the EFG method is improved by employing the improved moving least-squares (IMLS) approximation based on the shifted polynomial basis functions. The effectiveness of the IEFG method for the gfKdV equation is investigated by using some numerical examples. Meanwhile, the motion of single solitary wave and the interaction of two solitons are simulated using the IEFG method. 相似文献
12.
An improved element-free Galerkin method for solving the generalized fifth-order Korteweg–de Vries equation 下载免费PDF全文
In this paper, an improved element-free Galerkin (IEFG) method is proposed to solve the generalized fifth-order Korteweg-de Vries (gfKdV) equation. When the traditional element-free Galerkin (EFG) method is used to solve such an equation, unstable or even wrong numerical solutions may be obtained due to the violation of the consistency conditions of the moving least-squares (MLS) shape functions. To solve this problem, the EFG method is improved by employing the improved moving least-squares (IMLS) approximation based on the shifted polynomial basis functions. The effectiveness of the IEFG method for the gfKdV equation is investigated by using some numerical examples. Meanwhile, the motion of single solitary wave and the interaction of two solitons are simulated using the IEFG method. 相似文献
13.
A RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in Lagrangian coordinate 下载免费PDF全文
In this paper, Runge-Kutta Discontinuous Galerkin (RKDG) finite element method is presented to solve the one-dimensional inviscid compressible gas dynamic equations in Lagrangian coordinate. The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method. A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method. For multi-medium fluid simulation, the two cells adjacent to the interface are treated differently from other cells. At first, a linear Riemann solver is applied to calculate the numerical flux at the interface. Numerical examples show that there is some oscillation in the vicinity of the interface. Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical flux at the interface, which suppress the oscillation successfully. Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm. 相似文献
14.
In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wavesolutions for the generalized time-delayed Burgers-Fisher equation.A minor error in the previous article is clarified. 相似文献
15.
16.
In this paper, we will present a unified formulation of discontinuous Galerkin method (DGM) for Maxwell's equations in linear dispersive and lossy materials of Debye type and in the artificial perfectly matched layer (PML) regions. An auxiliary differential equation (ADE) method is used to handle the frequency-dependent constitutive relations with the help of auxiliary polarization currents in the computational and PML regions. The numerical flux for the dispersive lossy Maxwell's equations with the auxiliary polarization current variables is derived. Various numerical results are provided to validate the proposed formulation. 相似文献
17.
In this paper we develop a lattice Boltzmann model for the generalized Burgers-Huxley equation (GBHE). By choosing the proper time and space scales and applying the Chapman-Enskog expansion, the governing equation is recovered correctly from the lattice Boltzmann equation, and the local equilibrium distribution functions are obtained. Excellent agreement with the exact solution is observed, and better numerical accuracy is obtained than the available numerical result. The results indicate the present model is satisfactory and efficient. The method can also be applied to the generalized Burgers-Fisher equation and be extended to multidimensional cases. 相似文献