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Volume 10, Number 2, 2020, Pages 391-410                                                                DOI:10.11948/20170028
Solving an inverse problem for a generalized time-delayed Burgers-Fisher equation by Haar wavelet method
Saedeh Foadian,Reza Pourgholi,S. Hashem Tabasi,Hamed Zeidabadi
Keywords:Ill-posed inverse problems, Haar wavelet method, Tikhonov regularization method, error estimation, convergence analysis.
Abstract:
      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 $\Bigl(O\left(\frac{1}{2^{J+1}}\right)\Bigr)$, 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.
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