Mixed generalized Laguerre-Fourier spectral method for exterior problem of Navier-Stokes equations
Ben-Yu Guo Yu-Jian Jiao
In this paper, we investigate the mixed generalized Laguerre-Fourier spectral method and its applications to exterior problems of partial differential equations of fourth order. Some basic results on the mixed generalized Laguerre-Fourier orthogonal approximation are established, which play important roles in designing and analyzing various spectral methods for exterior problems of fourth order. As an important application, a mixed spectral scheme is proposed for the stream function form of the Navier-Stokes equations outside a disc. The numerical solution fulfills the compressibility automatically and keeps the same conservation property as the exact solution. The stability and convergence of proposed scheme are proved. Numerical results demonstrate its spectral accuracy in space, and coincide with the analysis very well.
keywords: Mixed generalized Laguerre-Fourier spectral method exterior problems of fourth order Navier-Stokes equations
A spectral collocation method for solving initial value problems of first order ordinary differential equations
Ben-Yu Guo Zhong-Qing Wang
We propose a spectral collocation method for solving initial value problems of first order ODEs, based on the Legendre-Gauss-Lobatto interpolation. This method is easy to be implemented and possesses the spectral accuracy. We also develop a multi-step version of this process, which is very available for long-time calculation. Numerical results demonstrate the high accuracy of suggested algorithms and coincide well with the theoretical analysis.
keywords: multi-step version Numerical method based on Legendre-Gauss-Lobatto collocation spectral accuracy. initial value problems of first order ODEs
Pseudospectral method using generalized Laguerre functions for singular problems on unbounded domains
Zhong-Qing Wang Ben-Yu Guo Yan-Na Wu
In this paper, we develop a pseudospectral method for differential equations defined on unbounded domains. We first introduce Gauss-type interpolations using a family of generalized Laguerre functions, and establish basic approximation results. Then we propose a pseudospectral method for differential equations on unbounded domains, whose coefficients may degenerate or grow up. As examples, we consider two model problems. The proposed schemes match the underlying problems properly and exhibit spectral accuracy. Numerical results demonstrate the efficiency of this new approach.
keywords: exterior problems. Gauss-type interpolations using generalized Laguerre functions pseudospectral method for singular differential equations on unbounded domains
Modified Chebyshev rational spectral method for the whole line
Guo Ben-Yu Wang Zhong-Qing
A modified Chebyshev rational orthogonal system on the whole line is introduced. A rational spectral scheme for the Korteweg de Vries equation on the whole line is constructed. The convergence is proved. The numerical results show its efficiency.
keywords: the whole line Korteweg de Vries equation. Modified Chebyshev rational approximation

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