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Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition
Author(s) -
Ramezani Mehdi,
Dehghan Mehdi,
Razzaghi Mohsen
Publication year - 2008
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.20230
Subject(s) - mathematics , discretization , variable (mathematics) , partial differential equation , finite difference , finite difference method , mathematical analysis , spectral method , finite difference coefficient , space (punctuation) , hyperbolic partial differential equation , work (physics) , finite difference scheme , order of accuracy , integral equation , finite element method , method of characteristics , mixed finite element method , mechanical engineering , linguistics , philosophy , physics , engineering , thermodynamics
In this work the combined finite difference and spectral methods have been proposed for the numerical solution of the one‐dimensional wave equation with an integral condition. The time variable is approximated using a finite difference scheme. But the spectral method is employed for discretizing the space variable. The main idea behind this approach is that we can get high‐order results. The new method is used for two test problems and the numerical results are obtained to support our theoretical expectations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007