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Error estimation of Hermite spectral method for nonlinear partial differential equations. (English) Zbl 0918.65069

A Hermite approximation scheme is constructed for the Burgers equation. First some inverse and imbedding inequalities are derived. The stability and convergence of the proposed scheme is shown. The techniques are also applicable to other nonlinear problems in unbounded domains.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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