Mathematics of Computation

Error estimation of Hermite spectral method for nonlinear partial differential equations

Author(s): Ben-yu Guo.
Journal: Math. Comp. 68 (1999), 1067-1078.
Posted: February 5, 1999
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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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