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Solving an inverse problem for a generalized time-delayed Burgers-Fisher equation by Haar wavelet method
Reza Pourgholi,Hamed Zeidabadi,Saedeh Foadian,S. Hashem Tabasi
Keywords:Ill-posed inverse problems, Haar wavelet method, Tikhonov regularization method, Error estimation, Convergence analysis.
      In this paper, a numerical method consists of combining Haar wavelet method and Tikhonov regularization method to determine unknown boundary condition and unknown nonlinear source term for the generalized time-delayed Burgers-Fisher equation using noisy data is presented. A stable numerical solution is determined for the problem. We also show that the rate of convergence of the method is as exponential (O ( 1/(2^(J+1)) )), where J is maximal level of resolution of wavelet. Some numerical results are reported to show the efficiency and robustness of the proposed approach for solving the inverse problems.