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Type: Artigo de periódico
Title: On mean value solutions for the Helmholtz equation on square grids
Author: do Val, JBR
Andrade, MG
Abstract: A numerical treatment for the boundary value, problem involving the Helmholtz equation Deltau - lambda(2)u = f is presented. The method is a five-point formula with an improved accuracy when compared with the usual finite difference method. Besides, the accuracy evaluation is provided in analytical form and the classical difference scheme is seen as a truncated series approximation to the present method. The idea comes from approximations to analytical solutions to the Dirichlet problem inside a ball, based on the Green identity. The homogeneous and the nonhomogeneous parts are evaluated in separate expressions, and the precision error yielded is of order O(h(2)). Some numerical examples and comparisons are presented. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
Subject: numerical approximation
finite difference method
partial differential equation
Helmholtz equation
Country: Holanda
Editor: Elsevier Science Bv
Citation: Applied Numerical Mathematics. Elsevier Science Bv, v. 41, n. 4, n. 459, n. 479, 2002.
Rights: fechado
Identifier DOI: 10.1016/S0168-9274(01)00127-1
Date Issue: 2002
Appears in Collections:Unicamp - Artigos e Outros Documentos

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