检索结果-南通市图书馆

A New pseudospectral Method for Calculations of Hydrogen Atom in Arbitrary External Fields

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2002年第1期37卷 15-20页

作者： QIAOHao－Xue LIBai－Wen WuhanInstituteofPhysicsandMathematics TheChineseAcademyofSciencesWuhan430071China

A new pseudospectral method was introduced to calculate wavefunctions and energy levels of hydrogen atom in arbitrary potential. Some results of hydrogen atom in uniform magnetic fields were presented, high accuracy of results was obtained with simple calculations, and our calculations show very fast convergence. It suggests a new methodfor calculations of hydrogen atom in external fields.

关键词： pseudospectral magnetic fields hydrogen

Multi-Domain Decomposition pseudospectral Method for Nonlinear Fokker-Planck Equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications on Applied Mathematics and Computation 2019年第2期1卷 231-252页

作者： Tao Sun Tian-jun Wang School of Statistics and Mathematics Shanghai Lixin University of Accounting and FinanceShanghai 201209China School of Mathematics and Statistics Henan University of Science and TechnologyLuoyang 471003China

Results on the composite generalized Laguerre-Legendre interpolation in unbounded domains are established. As an application,a composite Laguerre-Legendre pseudospectral scheme is presented for nonlinear Fokker-Planck equations on the whole line. The convergence and the stability of the proposed scheme are proved. Numerical results show the efficiency of the scheme and conform well to theoretical analysis.

关键词： Composite generalized Laguerre-Legendre pseudospectral approximation Nonlinear Fokker-Planck equations defined on unbounded domains Multi-domain decomposition pseudospectral method

FOURIER-CHEBYSHEV pseudospectral METHOD FOR THREE-DIMENSIONAL VORTICITY EQUATION WITH UNILATERALLY PERIODIC BOUNDARY CONDITION

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Numerical Mathematics A Journal of Chinese Universities(English Series) 1994年第2期3卷 216-242页

作者：郭本瑜李健曹卫明 Department of Mathematics Shanghai University of Science and Technology Shanghai 201800 PRC. Department of Mathematics Shanghai University of Science and Tech-nology Shanghai 201800 PRC

A Fourier-Chebyshev pseudospectral scheme is proposed for three-dimensionalvorticily equation with unilaterally periodic boundary condition. The generalized stability and convergence are analysed. The numerical result... 详细信息

关键词： Three-dimensional vorticity equation Fourier-Chebyshev pseudospectral approximation.

A GENERALIZED GAUSS-TYPE QUADRATURE FORMULA AND ITS APPLICATIONS TO pseudospectral METHOD

在线全文

学校读者我要写书评

暂无评论

Numerical Mathematics A Journal of Chinese Universities(English Series) 2002年第2期11卷 179-196页

作者：王立联郭本瑜王中庆 Department of Mathematics Laboratory of Computational Physics

A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.

关键词： generalized Gauss-type quadrature formula, pseudospectral method, K-S equa-tion.

THE CHEBYSHEV pseudospectral DOMAIN DECOMPO SITION METHOD FOR SOLVING TWO-DIMENSIONAL ELLIPTIC EQUATION

在线全文

学校读者我要写书评

暂无评论

Numerical Mathematics A Journal of Chinese Universities(English Series) 1996年第1期5卷 1-12页

作者：熊岳山 Department of Computer Science National University of Defense TechnologyChangsha410073

This paper ix devoted to establishment of the Chebyshev pseudospectral domain de-composition scheme for solving two-dimensional elliptic equation. By the generalized equivalent variatiunal form, we can get the stabili... 详细信息

关键词： Chebyshev pseudospectral method domain decomposition two-dimensional elliptic equation.

THE STRUCTURE-PRESERVING METHODS FOR THE DEGASPERIS-PROCESI EQUATION

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2019年第4期37卷 475-487页

作者： Yuze Zhang Yushun Wang Yanhong Yang Department of Applied Mathematics The Hongkong Polytechnic University China Jiangsu Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing 210023 China Department of Mathematics College of Taizhou Nanjing Normal University Taizhou 225300 China

This paper gives several structure-preserving schemes for the Degasperis-Procesi equation which has bi-Hamiltonian structures consisted of both complex and non-local Hamiltonian differential operators. For this sake, few structure-preserving schemes have been proposed so far. In our work, based on one of the bi-Hamiltonian structures, a symplectic scheme and two new energy-preserving schemes are constructed. The symplecticity comes straightly from the application of the implicit midpoint method on the semi-discrete system which is proved to remain Hamiltonian, while the energy conservation is derived by the combination of the averaged vector field method of second and fourth order, respectively. Some numerical results are presented to show that the three schemes do have the advantages in numerical stability, accuracy in long time computing and ability to preserve the invariants of the DP equation.

关键词： Degasperis-Procesi equation bi-Hamiltonian structure Structure-preserving scheme Fourier pseudospectral method

A hybrid method of fractional steps with predictor-corrector difference-pseudospectrum for numerical solution of the convection-dominated flow problems

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China Mathematics 1995年第7期38卷 838-852页

作者：王喜君张法高吴江航 Department of Mechanics Peking University. Beijing 100871 China Institute of Oceanology Chinese Academy of Sciences. Qingdao 266071 China

A fractional-step method of predictor-corrector difference-pseudospectrum with unconditional L2-stability and exponential convergence is presented. The stability and convergence of this method is strictly proved mathematically for a nonlinear convection-dominated flow. The error estimation is given and the superiority of this method is verified by numerical test.

关键词： convective domination fractional-step method predictor-corrector method pseudospectral method.

Truncated Gaussian RBF Differences are Always Inferior to Finite Differences of the Same Stencil Width

在线全文

学校读者我要写书评

暂无评论

Communications in Computational Physics 2009年第1期5卷 42-60页

作者： John P.Boyd Lei Wang Department of Atmospheric Oceanic and Space ScienceUniversity of MichiganAnn Arbor MI 48109USA Department of Mathematics and Program in Applied and Interdisciplinary Mathematics University of MichiganAnn Arbor MI 48109USA

Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ***,we compare one important scheme to ordinary finite differences by a mixture of numerical experiments and theoretical Fourier analysis,that is,by deriving and discussing analytical formulas for the error in differentiating exp(ikx)for arbitrary k.‘Truncated RBF differences”are derived from the same strategy as Fourier and Chebyshev pseudospectral methods:Differentiation of the Fourier,Chebyshev or RBF interpolant generates a differentiation matrix that maps the grid point values or samples of a function u(x)into the values of its derivative on the *** Fourier and Chebyshev interpolants,the action of the differentiation matrix can be computed indirectly but efficiently by the Fast Fourier Transform(FFT).For RBF functions,alas,the FFT is inapplicable and direct use of the dense differentiation matrix on a grid of N points is prohibitively expensive(O(N2))unless N is ***,for Gaussian RBFs,which are exponentially localized,there is another option,which is to truncate the dense matrix to a banded matrix,yielding“truncated RBF differences”.The resulting formulas are identical in form to finite differences except for the difference *** a grid of spacing h with the RBF asφ(x)=exp(−α^(2)(x/h)^(2)),d f dx(0)≈∑^(∞)_(m)=1 wm{f(mh)−f(−mh)},where without approximation wm=(−1)m+12α^(2)/sinh(mα^(2)).We derive explicit formula for the differentiation of the linear function,f(X)≡X,and the errors *** show that Gaussian radial basis functions(GARBF),when truncated to give differentiation formulas of stencil width(2M+1),are significantly less accurate than(2M)-th order finite differences of the same stencil *** error of the infinite series(M=∞)decreases exponentially asα→***,truncated GARBF series have a second error(truncation error)that grows exponentially asα→*** forα∼O(1)where the sum of these two errors is minimized,it is

关键词： pseudospectral radial basis function high order finite difference nonstandard finite differences spectral differences

Chebyshev Spectral Methods and the Lane-Emden Problem

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Numerical Mathematics(Theory,Methods and Applications) 2011年第2期4卷 142-157页

作者： John P.Boyd Department of Atmospheric Oceanic and Space ScienceUniversity of Michigan2455 Hayward AvenueAnn ArborMI 48109-2143USA

The three-dimensional spherical polytropic Lane-Emden problem is yr r+(2/r)y_(r)+y^(m)=0,y(0)=1,y_(r)(0)=0 where m∈[0,5]is a constant *** domain is r∈[0,ξ]whereξis the first root of y(r).We recast this as a nonlinear eigenproblem,with three boundary conditions andξas the eigenvalue allowing imposition of the extra boundary condition,by making the change of coordinate x≡r/ξ:y_(xx)+(2/x)y_(x)+ξ^(2) y^(m)=0,y(0)=1,y_(x)(0)=0,y(1)=*** find that a Newton-Kantorovich iteration always converges from an m-independent starting point y^((0))(x)=cos([π/2]x),ξ^((0))=*** apply a Chebyshev pseudospectral method to discretize *** Lane-Emden equation has branch point singularities at the endpoint x=1 whenever m is not an integer;we show that the Chebyshev coefficients are a_(n)∼constant/n^(2m+5) as n→∞.However,a Chebyshev truncation of N=100 always gives at least ten decimal places of accuracy—much more accuracy when m is an *** numerical algorithm is so simple that the complete code(in Maple)is given as a one page table.

关键词： Lane-Emden Chebyshev polynomial pseudospectral