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

Funaro, Daniele; Kavian, Otared

Math. Comput. 57, No. 196, 597-619 (1991).

(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.)

Keywords:

unbounded domain; spectral methods; stability; pseudospectral approximations; convergence estimates

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