共查询到20条相似文献,搜索用时 93 毫秒
1.
研究多维区域中非线性偏微分方程的谱与拟谱方法.建立了修正Laguerre正交逼近与插值结果,这些结果对于建立和分析无界区域中的数值方法起着重要的作用.作为结果的一个应用,研究了二维无界区域中的Logistic方程的修正Laguerre谱格式,证明了它的稳定性和收敛性.数值试验结果表明所提出方法具有很高的精度,与理论分析结果完全吻合. 相似文献
2.
3.
计算流体力学中的谱方法 总被引:1,自引:0,他引:1
本文论及偏微分方程数值解中的谱方法的理论基础和数值实现.评述近年来有关谱方法的最主要的几个研究领域,着重讨论区域分解技术,不同数学模型的耦合以及不同离散方法的耦合问题,并介绍一些最新结果. 相似文献
4.
研究应用广义Laguerre函数的四阶非线性偏微分方程外部问题混合谱方法.构造了圆外Navier-Stokes方程流函数形式的混合谱方法,数值结果显示了该方法在空间方向的谱精度. 相似文献
5.
六边形Fourier谱方法 总被引:1,自引:0,他引:1
首先,建立了晶格Fourier分析的一般理论,并具体研究了六边形区域上周期函数的数值逼近.在此基础上,提出了六边形区域上的椭圆型偏微分方程的周期问题求解的六边形Fourier谱方法,设计了相应谱格式快速实现算法,建立了Fourier谱方法的稳定性与收敛性理论.同方形区域上的经典Fourier谱方法一样,六边形Fourier谱方法可以充分利用快速Fourier变换,并具备了"无穷阶"的谱收敛速度. 相似文献
6.
针对无界区域上Korteweg.-de Vries(KdV)方程构造了时空全离散的ChebyshevHermite谱配置格式,即在空间方向上采用Hermite谱配置方法离散,时间方向上采用Chebyshev谱配置方法离散.提出了一个简单迭代算法,该算法非常适合并行计算.数值结果显示了此算法的有效性. 相似文献
7.
对半无界区域上的三阶方程提出了Laguerre-Petrov-Galerkin谱逼近方法,选取了相同的试探空间和检验空间.通过构造该空间上的基函数,离散问题所对应的线性系统的系数矩阵是半稀疏的.数值算例验证了该方法的有效性和高精度. 相似文献
8.
1 引言无界区域问题的有理谱方法已经得到广泛地应用.它有很多优点,特别是我们不需要添加任何人工边界以及作任何变量变换就可以直接逼近微分方程.此外,Jacobi 有理谱方法可以用来数值求解变系数的微分方程,如金融数学中的基本方程-Black- 相似文献
9.
主要研究两同心球所界球形区域上偏微分方程的谱方法,建立了与区域形状相适应的混合Legendre-球面调和正交逼近的部分结果,在此基础上提出了数值求解两同心球所界球形区域上Fisher型方程的混合Legendre-球面调和谱格式,并分别给出了格式的收敛性及相关的数值结果. 相似文献
10.
11.
Modified Laguerre pseudospectral method refined by multidomain Legendre pseudospectral approximation
A modified Laguerre pseudospectral method is proposed for differential equations on the half-line. The numerical solutions are refined by multidomain Legendre pseudospectral approximation. Numerical results show the spectral accuracy of this approach. Some approximation results on the modified Laguerre and Legendre interpolations are established. The convergence of proposed method is proved. 相似文献
12.
GUO BenYu 《中国科学 数学(英文版)》2013,56(12):2411-2438
In this paper,we review some results on the spectral methods.We frst consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems,including degenerated and singular diferential equations.Then we present the generalized Jacobi quasi-orthogonal approximation and its applications to the spectral element methods for high order problems with mixed inhomogeneous boundary conditions.We also discuss the related spectral methods for non-rectangular domains and the irrational spectral methods for unbounded domains.Next,we consider the Hermite spectral method and the generalized Hermite spectral method with their applications.Finally,we consider the Laguerre spectral method and the generalized Laguerre spectral method for many problems defned on unbounded domains.We also present the generalized Laguerre quasi-orthogonal approximation and its applications to certain problems of non-standard type and exterior problems. 相似文献
13.
Spectral methods using generalized Laguerre functions are proposed for second-order equations under polar (resp. spherical) coordinates in ?2 (resp. ?3) and fourth-order equations on the half line. Some Fourier-like Sobolev orthogonal basis functions are constructed for our Laguerre spectral methods for elliptic problems. Optimal error estimates of the Laguerre spectral methods are obtained for both second-order and fourth-order elliptic equations. Numerical experiments demonstrate the effectiveness and the spectral accuracy. 相似文献
14.
We use the Weyl correspondence approach to investigate the spectral operators of the Laguerre and the Kautz systems. We show that the basic functions in the Laguerre and the Kautz systems are the eigenvectors of modified Sturm-Liouville operators. The results are further generalized to multiple parameters of one complex variable in both the unit disc and the upper half-plane contexts. 相似文献
15.
Efficient Laguerre and Hermite Spectral Methods for Odd-Order Differential Equations in Unbounded Domains 下载免费PDF全文
Laguerre dual-Petrov-Galerkin spectral methods and Hermite Galerkin spectral methods for solving odd-order differential equations in unbounded domains are
proposed. Some Sobolev bi-orthogonal basis functions are constructed which lead to
the diagonalization of discrete systems. Numerical results demonstrate the effectiveness of the suggested approaches. 相似文献
16.
A fully diagonalized spectral method using generalized Laguerre functions is proposed and analyzed for solving elliptic equations on the half line. We first define the generalized Laguerre functions which are complete and mutually orthogonal with respect to an equivalent Sobolev inner product. Then the Fourier-like Sobolev orthogonal basis functions are constructed for the diagonalized Laguerre spectral method of elliptic equations. Besides, a unified orthogonal Laguerre projection is established for various elliptic equations. On the basis of this orthogonal Laguerre projection, we obtain optimal error estimates of the fully diagonalized Laguerre spectral method for both Dirichlet and Robin boundary value problems. Finally, numerical experiments, which are in agreement with the theoretical analysis, demonstrate the effectiveness and the spectral accuracy of our diagonalized method. 相似文献
17.
Qingqu Zhuang 《Journal of Computational and Applied Mathematics》2010,235(3):615-630
Some Legendre spectral element/Laguerre spectral coupled methods are proposed to numerically solve second- and fourth-order equations on the half line. The proposed methods are based on splitting the infinite domain into two parts, then using the Legendre spectral element method in the finite subdomain and Laguerre method in the infinite subdomain. C0 or C1-continuity, according to the problem under consideration, is imposed to couple the two methods. Rigorous error analysis is carried out to establish the convergence of the method. More importantly, an efficient computational process is introduced to solve the discrete system. Several numerical examples are provided to confirm the theoretical results and the efficiency of the method. 相似文献
18.
A spectral method for solving the 2D Maxwell equations with relaxation of electromagnetic parameters is presented. The method is based on an expansion of the solution in terms of Laguerre functions in time. The operation of convolution of functions, which is part of the formulas describing the relaxation processes, is reduced to a sum of products of the harmonics. The Maxwell equations transform to a system of linear algebraic equations for the solution harmonics. In the algorithm, an inner parameter of the Laguerre transformis used. With large values of this parameter, the solution is shifted to high harmonics. This is done to simplify the numerical algorithm and to increase the efficiency of the problem solution. Results of a comparison of the Laguerre method and a finite-difference method in accuracy both for a 2D medium structure and a layered medium are given. Results of a comparison of the spectral and finite-difference methods in efficiency for axial and plane geometries of the problem are presented. 相似文献
19.
Composite generalized Laguerre spectral method for nonlinear Fokker–Planck equations on the whole line 下载免费PDF全文
Tian‐jun Wang 《Mathematical Methods in the Applied Sciences》2017,40(5):1462-1474
In this paper, we propose a composite Laguerre spectral method for the nonlinear Fokker–Planck equations modelling the relaxation of fermion and boson gases. A composite Laguerre spectral scheme is constructed. Its convergence is proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. Some results on the Laguerre approximation and techniques used in this paper are also applicable to other nonlinear problems on the whole line. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
20.
F. Talay Akyildiz 《Mathematical Methods in the Applied Sciences》2007,30(17):2263-2277
A Laguerre–Galerkin method is proposed and analysed for the Stokes' first problem of a Newtonian fluid in a non‐Darcian porous half‐space on a semi‐infinite interval. It is well known that Stokes' first problem has a jump discontinuity on boundary which is the main obstacle in numerical methods. By reformulating this equation with suitable functional transforms, it is shown that the Laguerre–Galerkin approximations are convergent on a semi‐infinite interval with spectral accuracy. An efficient and accurate algorithm based on the Laguerre–Galerkin approximations of the transformed equations is developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献