Error estimation of Hermite spectral method

for nonlinear partial differential equations

Author:
Ben-yu Guo

Journal:
Math. Comp. **68** (1999), 1067-1078

DOI:
https://doi.org/10.1090/S0025-5718-99-01059-5

Published electronically:
February 5, 1999

MathSciNet review:
1627789

Full-text PDF

Abstract | References | Additional Information

Abstract: 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.

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Additional Information

**Ben-yu Guo**

Affiliation:
Department of Mathematics, Shanghai University, Jiading Campus, Shanghai, 201800, China

Address at time of publication:
Department of Mathematics, Shanghai Normal University, Shanghai, China

Email:
byquo@quomai.sh.cn

DOI:
https://doi.org/10.1090/S0025-5718-99-01059-5

Keywords:
Hermite approximation, Burgers equation, error estimations

Received by editor(s):
October 16, 1997

Received by editor(s) in revised form:
January 2, 1998

Published electronically:
February 5, 1999

Article copyright:
© Copyright 1999
American Mathematical Society