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Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains. (English) Zbl 1087.65097

The authors discuss the Hermite spectral methods with a time dependent scaling for parabolic equations. After an initial discussion of the basic properties a stability and convergence analysis is established by theorems and lemmas. Finally, a number of experiments are performed for illustration.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
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