NUMERICAL SOLUTION OF THE INVERSE GARDNER EQUATION

NUMERICAL SOLUTION OF THE INVERSE GARDNER EQUATION

S. Foadian, R. Pourgholi, M. G. Baladezaei

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Abstract

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-speci ed 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( x). The e ciency 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.