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RESOLUTION OF AN INVERSE PROBLEM BY HAAR BASIS AND LEGENDRE WAVELET METHODS

2013; World Scientific; Volume: 11; Issue: 05 Linguagem: Inglês

10.1142/s0219691313500343

1793-690X

Reza Pourgholi, Amin Esfahani, Saedeh Foadian, SONA PAREHKAR,

Sparse and Compressive Sensing Techniques

In this paper, two numerical methods are presented to solve an ill-posed inverse problem for Fisher's equation using noisy data. These two methods are the Haar basis and the Legendre wavelet methods combined with the Tikhonov regularization method. A sensor located at a point inside the body is used and u(x, t) at a point x = a, 0 < a < 1 is measured and these methods are applied to the inverse problem. We also show that an exponential rate of convergence of these methods. In fact, this work considers a comparative study between the Haar basis and the Legendre wavelet methods to solve some ill-posed inverse problems. Results show that an excellent estimation of the unknown function of the inverse problem which have been obtained within a couple of minutes CPU time at Pentium(R) Dual-Core CPU 2.20 GHz.