Numerical Methods for Partial Differential Equations · 2007 · 21 citations · 12 references
ComputingPhysicsComputational Heat TransferComputational PhysicsDifferential EquationsConvergence AnalysisNumerical ConvergenceNumerical Methods For Differential EquationsNumerical StabilitySpectral AnalysisSpectral MethodsHeat EquationHermite FunctionsStability Of Numerical Schemes
Abstract A stabilized Hermite spectral method, which uses the Hermite polynomials as trial functions, is presented for the heat equation and the generalized Burgers equation in unbounded domains. In order to overcome instability that may occur in direct Hermite spectral methods, a time‐dependent scaling factor is employed in the Hermite expansions. The stability of the scheme is examined and optimal error estimates are derived. Numerical experiments are given to confirm the theoretical results.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
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