论文信息 - Error estimation of Hermite spectral method for nonlinear partial differential equations

Error estimation of Hermite spectral method for nonlinear partial differential equations

Hermite approximation is investigated. Some inverse inequalities, imbedding inequalities and approximation results are obtained. A Hermite spectral scheme is constructed for Burgers equation. The stability and convergence of the proposed scheme are proved strictly. The techniques used in this paper are also applicable to other nonlinear problems in unbounded domains.

Ben-yu Guo | B. Guo

[1] D. Funaro,et al. Approximation of some diffusion evolution equations in unbounded domains by hermite functions , 1991 .

[2] R. Courant,et al. Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[3] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.

[4] Y. Maday,et al. Une réhabilitation des méthodes spectrales de type Laguerre , 1985 .

[5] Catherine Mavriplis. Polynomials for infinite-domain spectral elements , 1989 .

[6] Albert Falqués,et al. Some spectral approximations for di erential equations in un-bounded domains , 1992 .

[7] J. Boyd. Spectral methods using rational basis functions on an infinite interval , 1987 .

[8] D. Funaro,et al. Laguerre spectral approximation of elliptic problems in exterior domains , 1990 .

[9] J. A. C. Weideman,et al. The eigenvalues of Hermite and rational spectral differentiation matrices , 1992 .