2010
DOI: 10.1137/090773581
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Generalized Hermite Spectral Method and its Applications to Problems in Unbounded Domains

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Cited by 42 publications
(28 citation statements)
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“…And it is as we expected that the time-dependent scaling factor yields better resolution than the constant one, i.e. the scheme in [26,17]. From the viewpoint of computational complexity, our scheme can be implemented straight-forward without any variable transformation.…”
Section: 1mentioning
confidence: 64%
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“…And it is as we expected that the time-dependent scaling factor yields better resolution than the constant one, i.e. the scheme in [26,17]. From the viewpoint of computational complexity, our scheme can be implemented straight-forward without any variable transformation.…”
Section: 1mentioning
confidence: 64%
“…This equivalence can be extended trivially to where β = 0, by mimicking the proof of Lemma 2.2-2.3 in [26] with x replaced by (x − β). From the definition of || · || P,r,α , it is clear to see that the larger r is, the smaller space H r,α is, and the smoother the functions are.…”
Section: 2mentioning
confidence: 91%
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“…In [12], making use of the idea of [1,8], we present a Hermite function system with weight ω(x) ≡ 1 and established the spectral approximate theory for the whole line. The aim of this paper is to develop the Hermite pseudospectral method.…”
Section: Introductionmentioning
confidence: 99%