共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
《Journal of Computational and Applied Mathematics》2005,181(2):342-363
A new family of generalized Laguerre polynomials is introduced. Various orthogonal projections are investigated. Some approximation results are established. As an example of their important applications, the mixed spherical harmonic-generalized Laguerre approximation is developed. A mixed spectral scheme is proposed for a three-dimensional model problem. Its convergence is proved. Numerical results demonstrate the high accuracy of this new spectral method. 相似文献
3.
New unconditionally stable scheme for telegraph equation based on weighted Laguerre polynomials 下载免费PDF全文
This article proposes a new unconditionally stable scheme to solve one‐dimensional telegraph equation using weighted Laguerre polynomials. Unlike other numerical schemes, the time derivatives in the equation can be expanded analytically based on the Laguerre polynomials and basis functions. By applying a Galerkin temporal testing procedure and using the orthogonal property of weighted Laguerre polynomials, the time variable can be eliminated from computations, which results in an implicit equation. After solving the equation recursively one can obtain the numerical results of telegraph equation by using the expanded coefficients. Some numerical examples are considered to validate the accuracy and stability of this proposed scheme, and the results are compared with some existing numerical schemes.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1603–1615, 2017 相似文献
4.
A stair Laguerre pseudospectral method is proposed for numerical solutions of differential equations on the half line. Some
approximation results are established. A stair Laguerre pseudospcetral scheme is constructed for a model problem. The convergence
is proved. The numerical results show that this new method provides much more accurate numerical results than the standard
Laguerre spectral method.
Dedicated to Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 65N35, 41A10.
Li-lian Wang: The work of this author is partially supported by The Shanghai Natural Science Foundation N. 00JC14057, The
Shanghai Natural Science Foundation for Youth N. 01QN85 and The Special Funds for Major Specialities of Shanghai Education
Committee.
Ben-yu Guo: The work of this author is partially supported by The Special Funds for Major State Basic Research Projects of
China G1999032804, The Shanghai Natural Science Foundation N. 00JC14057 and The Special Funds for Major Specialities of Shanghai
Education Committee. 相似文献
5.
A. F. Mastryukov 《Numerical Analysis and Applications》2016,9(4):299-311
In this paper, a solution to a two-dimensional wave equation using the Laguerre transform is considered. Optimal parameters of finite difference schemes for this equation are obtained. Numerical values of these optimal parameters are specified. Second-order finite difference schemes with the optimal parameters provide an accuracy of solving the equations close to that provided by a fourth-order scheme. It is shown that using the Laguerre decomposition can reduce the number of optimal parameters in comparison with using the Fourier decomposition. This simplifies the finite difference schemes and decreases the number of calculations, that is, makes the algorithm more efficient. 相似文献
6.
Mustafa Gülsu Burcu GürbüzYalç?n Öztürk Mehmet Sezer 《Applied mathematics and computation》2011,217(15):6765-6776
This paper presents a numerical method for the approximate solution of mth-order linear delay difference equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. The aim of this article is to present an efficient numerical procedure for solving mth-order linear delay difference equations with variable coefficients. Our method depends mainly on a Laguerre series expansion approach. This method transforms linear delay difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple. 相似文献
7.
Yizhen Huang Yangjing Long 《Communications in Nonlinear Science & Numerical Simulation》2007,12(8):1584-1603
We use four orthogonal polynomial series, Legendre, Chebyshev, Hermite and Laguerre series, to approximate the non-homogeneous term for the precise time integration and incorporate them with the dimensional expanding technique. They are applied to various structures subjected to transient dynamic loading together with Fourier and Taylor approximation proposed in previous works. Numerical examples show that all six methods are efficient and have reasonable precision. In particular, Legendre approximation has much higher precision and better convergence; Chebyshev approximation is also good, but only slightly inferior to Legendre approximation. The other four approximation methods usually produce results with errors hundreds of thousands of times larger. Hermite and Laguerre approximation may be useful for some special non-homogeneous terms, but do not work sufficiently well in our numerical examples. Other contributions of this paper include, a Dynamic Programming scheme for computing series coefficients, a general formula to find the assistant matrix for any polynomial series. 相似文献
8.
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
9.
A composite LegendreLaguerre pseudospectral approximationin unbounded domains is developed. Some approximation resultsare obtained. As an application, a composite pseudospectralscheme is proposed for the Burgers equation on the half-line.The stability and convergence of the scheme are proved. By choosingappropriate base functions, the resulting system of this methodhas a sparse structure and can be solved in parallel. Numericalresults are given to show the efficiency of this new method. 相似文献
10.
《Journal de Mathématiques Pures et Appliquées》2005,84(3):375-405
We study different Sobolev spaces associated with multidimensional Laguerre expansions. To do this we establish an analogue of P.A. Meyer's multiplier theorem, prove some transference results between higher order Riesz–Hermite and Riesz–Laguerre transforms, and introduce fractional derivatives and integrals corresponding to the Laguerre setting. Hypercontractivity of the Laguerre semigroups and Calderón's reproduction formula are also discussed. 相似文献
11.
A Spectral Element/Laguerre Coupled Method to the Elliptic Helmholtz Problem on the Half Line 总被引:1,自引:1,他引:0
Qingqu Zhuang Chuanju Xu 《高等学校计算数学学报(英文版)》2006,15(3):193-208
A Legendre spectral element/Laguerre coupled method is proposed to numerically solve the elliptic Helmholtz problem on the half line. Rigorous analysis is carried out to establish the convergence of the method. Several numerical examples are provided to confirm the theoretical results. The advantage of this method is demonstrated by a numerical comparison with the pure Laguerre method. 相似文献
12.
若超曲面的Laguerre形式为零且Laguerre第二基本形式的特征值(称为Laguerre主曲率)为常数,则称超曲面为Laguerre等参超曲面.对R~6中的Laguerre等参超曲面进行了研究,得到了分类定理. 相似文献
13.
We propose a unified approach to the theory of Riesz transforms and conjugacy in the setting of multi-dimensional orthogonal
expansions. The scheme is supported by numerous examples concerning, in particular, the classical orthogonal expansions in
Hermite, Laguerre, and Jacobi polynomials. A general case of expansions associated to a regular or singular Sturm-Liouville
problem is also discussed. 相似文献
14.
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
15.
In this paper, the Laguerre–Sheffer polynomials are introduced by using the monomiality principle formalism and operational methods. The generating function for the Laguerre–Sheffer polynomials is derived and a correspondence between these polynomials and the Sheffer polynomials is established. Further, differential equation, recurrence relations and other properties for the Laguerre–Sheffer polynomials are established. Some concluding remarks are also given. 相似文献
16.
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
17.
Ben-yuGuo JieShen Cheng-longXu 《计算数学(英文版)》2005,23(2):113-130
Approximations using the generalized Laguerre polynomials are investigated in this paper. Error estimates for various orthogonal projections are established. These estimates generalize and improve previously published results on the Laguerre approximations. As an example of applications, a mixed Laguerre-Fourier spectral method for the Helmholtz equation in an exterior domain is analyzed and implemented. The proposed method enjoys optimal error estimates, and with suitable basis functions, leads to a sparse and symmetric linear system. 相似文献
18.
Zhong-qing Wang 《Journal of Computational and Applied Mathematics》2011,235(10):3229-3237
In this paper, we propose a Laguerre spectral method for solving Neumann boundary value problems. This approach differs from the classical spectral method in that the homogeneous boundary condition is satisfied exactly. Moreover, a tridiagonal matrix is employed, instead of the full stiffness matrix encountered in the classical variational formulation of such problems. For analyzing the numerical errors, some basic results on Laguerre approximations are established. The convergence is proved. The numerical results demonstrate the efficiency of this approach. 相似文献
19.
Günter F. Steinke 《Results in Mathematics》2010,57(1-2):43-51
We characterize the non-classical 4-dimensional elation Laguerre planes as precisely those 4-dimensional Laguerre planes of Kleinewillinghöfer type I.D.1. Furthermore, in the class of 2- or 4-dimensional Laguerre planes or finite Laguerre planes of odd order, the non-miquelian elation Laguerre planes are precisely the Laguerre planes of Kleinewillinghöfer type D. 相似文献
20.
Shuhuang Xiang 《Journal of Mathematical Analysis and Applications》2012,393(2):434-444
In this paper, we present asymptotic analysis on the coefficients of functions expanded in forms of Laguerre or Hermite polynomial series, which shows the decay of the coefficients and derives new error bounds on the truncated series. Moreover, by applying the asymptotics, new estimates on the errors for Gauss–Laguerre, Radau–Laguerre and Gauss–Hermite quadrature are deduced. These results show that Gauss–Laguerre-type and Gauss-Hermite-type quadratures are nearly of same convergence rates. 相似文献