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.
Reviewer: W.Heinrichs (Essen)
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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