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Legendre multiscaling functions for solving the one‐dimensional parabolic inverse problem
Author(s) -
Yousefi S.A.,
Dehghan Mehdi
Publication year - 2009
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.20430
Subject(s) - legendre polynomials , mathematics , legendre wavelet , inverse problem , inverse , partial differential equation , partial derivative , algebraic equation , galerkin method , algebraic number , mathematical analysis , finite element method , geometry , computer science , discrete wavelet transform , physics , wavelet transform , nonlinear system , quantum mechanics , artificial intelligence , wavelet , thermodynamics
An inverse problem concerning diffusion equation with a source control parameter is investigated. The approximation of the problem is based on the Legendre multiscaling basis. The properties of Legendre multiscaling functions are first presented. These properties together with Galerkin method are then utilized to reduce the inverse problem to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009