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Solving an inverse problem for a generalized time-delayed Burgers-Fisher equation by Haar wavelet method |
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| Authors: | Saedeh Foadian Reza Pourgholi S Hashem Tabasi and Hamed Zeidabadi |
| Institution: | School of Mathematics and Computer Science, Damghan University, P.O.Box 36715- 364, Damghan, Iran.,School of Mathematics and Computer Science, Damghan University, P.O.Box 36715- 364, Damghan, Iran.,School of Mathematics and Computer Science, Damghan University, P.O.Box 36715- 364, Damghan, Iran. and School of Mathematics and Computer Science, Damghan University, P.O.Box 36715- 364, Damghan, Iran. |
| 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. |
| Keywords: | Ill-posed inverse problems Haar wavelet method Tikhonov regularization method error estimation convergence analysis |
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