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A new wavelet method for solving the Helmholtz equation with complex solution
Author(s) -
Heydari M. H.,
Hooshmandasl M. R.,
Maalek Ghaini F. M.,
Fatehi Marji M.,
Dehghan R.,
Memarian M. H.
Publication year - 2016
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.22022
Subject(s) - helmholtz equation , mathematics , wavelet , algebraic equation , partial differential equation , variety (cybernetics) , boundary value problem , helmholtz free energy , mathematical analysis , computer science , artificial intelligence , statistics , physics , nonlinear system , quantum mechanics
The Helmholtz equation which is very important in a variety of applications, such as acoustic cavity and radiation wave, has been greatly considered in recent years. In this article, we propose a new efficient computational method based on the Legendre wavelets (LWs) expansion together with their operational matrices of integration and differentiation to solve this equation with complex solution. Because of the fact that both of the operational matrices of integration and differentiation are used in the proposed method, the boundary conditions are taken into account automatically. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifies the problems. As an applied example, “propagation of plane waves” is investigated to demonstrate the validity and applicability of the presented method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 741–756, 2016