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A stabilized Hermite spectral method for second‐order differential equations in unbounded domains
Author(s) -
Ma Heping,
Zhao Tinggang
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20203
Subject(s) - hermite polynomials , mathematics , hermite spline , hermite interpolation , partial differential equation , mathematical analysis , order (exchange) , stability (learning theory) , differential equation , spectral method , statistics , finance , machine learning , computer science , smoothing spline , economics , bilinear interpolation , spline interpolation
A stabilized Hermite spectral method, which uses the Hermite polynomials as trial functions, is presented for the heat equation and the generalized Burgers equation in unbounded domains. In order to overcome instability that may occur in direct Hermite spectral methods, a time‐dependent scaling factor is employed in the Hermite expansions. The stability of the scheme is examined and optimal error estimates are derived. Numerical experiments are given to confirm the theoretical results.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007