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Spectral methods based on Hermite functions for linear hyperbolic equations
Author(s) -
Aguirre Julián,
Rivas Judith
Publication year - 2012
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.20699
Subject(s) - mathematics , hermite polynomials , mathematical analysis , hyperbolic partial differential equation , scalar (mathematics) , partial differential equation , domain (mathematical analysis) , convergence (economics) , rate of convergence , geometry , channel (broadcasting) , engineering , electrical engineering , economics , economic growth
We consider the approximation by spectral and pseudo‐spectral methods of the solution of the Cauchy problem for a scalar linear hyperbolic equation in one space dimension posed in the whole real line. To deal with the fact that the domain of the equation is unbounded, we use Hermite functions as orthogonal basis. Under certain conditions on the coefficients of the equation, we prove the spectral convergence rate of the approximate solutions for regular initial data in a weighted space related to the Hermite functions. Numerical evidence of this convergence is also presented. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012