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- W2078959912 abstract "Although Hermite functions were widely used for many practical problems, numerical experiments with the standard (normalized) Hermite functions $psi _n (v)$ worked poorly in the sense that too many Hermite functions are required to solve differential equations. In order to obtain accurate numerical solutions, it is necessary to choose a scaling factor $alpha $ and use $psi _n (alpha v)$ as the basis functions. In this paper the scaling factors are given for functions that are of Gaussian type, which have finite supports $[ - M,M]$. The scaling factor used is $max _{0 leqq j leqq N} { gamma _j } / M$, where ${ gamma _j } _{j = 0}^N $ are the roots of $psi _{N + 1} (v)$ and $N + 1$ is the number of the truncated terms used. The numerical results show that after using this scaling factor, only reasonable numbers of the Hermite functions are required to solve differential equations." @default.
- W2078959912 created "2016-06-24" @default.
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- W2078959912 date "1993-05-01" @default.
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- W2078959912 title "The Hermite Spectral Method for Gaussian-Type Functions" @default.
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- W2078959912 doi "https://doi.org/10.1137/0914038" @default.
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