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Approximation of some diffusion evolution equations in unbounded domains by Hermite functions. (English) Zbl 0764.35007

(Author’s abstract.) Spectral and pseudospectral approximations of the heat equation are analyzed. The solution is represented in a suitable basis constructed with Hermite polynomials. Stability and convergence estimates are given and numerical tests are discussed.
Reviewer: St.Mika (Plzen)

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
35K05 Heat equation
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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