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

doi:10.11948/20170028

2020 Volume 10 Issue 2

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Saedeh Foadian, Reza Pourgholi, S. Hashem Tabasi, Hamed Zeidabadi. SOLVING AN INVERSE PROBLEM FOR A GENERALIZED TIME-DELAYED BURGERS-FISHER EQUATION BY HAAR WAVELET METHOD[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 391-410. doi: 10.11948/20170028

Citation:

Saedeh Foadian, Reza Pourgholi, S. Hashem Tabasi, Hamed Zeidabadi. SOLVING AN INVERSE PROBLEM FOR A GENERALIZED TIME-DELAYED BURGERS-FISHER EQUATION BY HAAR WAVELET METHOD[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 391-410. doi: 10.11948/20170028

SOLVING AN INVERSE PROBLEM FOR A GENERALIZED TIME-DELAYED BURGERS-FISHER EQUATION BY HAAR WAVELET METHOD

1.
School of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364, Damghan, Iran

Corresponding author: Email address:pourgholi@du.ac.ir (R. Pourgholi) Tel.: +982335220092. Fax: +982335235316

Abstract

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.
- Ill-posed inverse problems /
- Haar wavelet method /
- Tikhonov regularization method /
- error estimation /
- convergence analysis
MSC: 65N20, 65N21, 65M32, 35K05

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References

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