NUMERICAL SOLUTION OF THE INVERSE GARDNER EQUATION

In this paper, the numerical solution of the inverse Gardner equation will be considered. The Haar wavelet collocation method (HWCM) will be used to determine the unknown boundary condition which is estimated from an over-specified condition at a boundary. In this regard, we apply the HWCM for discr...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 2; p. 649
Main Authors Foadian, S, Pourgholi, R, Baladezaei, M. G
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.04.2023
Elman Hasanoglu
Subjects
Algorithms
Applied mathematics
Boundary conditions
Collocation methods
Differential equations, Partial
Integral equations
Integrals
Inverse problems
Mathematical research
Numerical analysis
Physics
Quantum field theory
Regularization methods
Iran
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Summary:In this paper, the numerical solution of the inverse Gardner equation will be considered. The Haar wavelet collocation method (HWCM) will be used to determine the unknown boundary condition which is estimated from an over-specified condition at a boundary. In this regard, we apply the HWCM for discretizing the space derivatives and then use a quasilinearization technique to linearize the nonlinear term in the equations. It is proved that the proposed method has the order of convergence O([DELTA]x). The efficiency and robustness of the proposed approach for solving the inverse Gardner equation are demonstrated by one numerical example. Keywords: Haar wavelet, Ill-posed inverse problems, Quasilinearization technique, The Tikhonov regularization method. AMS Subject Classification: 65M32, 65T60.
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content type line 14
ISSN:2146-1147
2146-1147