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A Crank‐Nicolson and ADI Galerkin method with quadrature for hyperbolic problems
Author(s) -
Ganesh M.,
Mustapha K.
Publication year - 2005
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.20027
Subject(s) - mathematics , partial derivative , quadrature (astronomy) , crank–nicolson method , partial differential equation , boundary value problem , hyperbolic partial differential equation , galerkin method , scheme (mathematics) , mathematical analysis , finite element method , physics , electrical engineering , engineering , thermodynamics
We propose, analyze, and implement fully discrete two‐time level Crank‐Nicolson methods with quadrature for solving second‐order hyperbolic initial boundary value problems. Our algorithms include a practical version of the ADI scheme of Fernandes and Fairweather [SIAM J Numer Anal 28 (1991), 1265–1281] and also generalize the methods and analyzes of Baker [SIAM J Numer Anal 13 (1976), 564–576] and Baker and Dougalis [SIAM J Numer Anal 13 (1976), 577–598]. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005