Mathematics of Computation · 1999 · 148 citations · 9 references
ComputingPhysicsComputational MechanicsConvergence AnalysisError EstimationNumerical ConvergencePartial Differential EquationsSpectral MethodsSpectral TheoryElliptic Partial Differential EquationsError Estimation For Nonlinear ProblemsEstimation ErrorInverse Problems In Partial Differential EquationsNonlinear Partial Differential EquationsSpectral ApproximationSpectral ConvergenceStability Of Partial Differential Equations
The techniques used in this paper are also applicable to other nonlinear problems in unbounded domains. Hermite approximation is investigated. A Hermite spectral scheme is constructed for the Burgers equation. The authors establish inverse and embedding inequalities, approximation results, and prove strict stability and convergence of the Hermite spectral scheme.
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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