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Numerical solution of two-dimensional inverse time-fractional diffusion problem with non-local boundary condition using a-polynomials

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Abstract

In this paper, we obtain the numerical solution of two-dimensional inverse time-fractional diffusion problem with non-local boundary condition using a-polynomials. These polynomials are equipped with an unknown parameter a that is obtained by collocation and least squares methods. In fact, the optimal parameter a is replaced in the a-polynomials, and then with these polynomials that no longer have the a parameter, the numerical solution is approximated. Time discretization of the equation is performed by \({L_1}\) method. The convergence theorem for a-polynomials has been proved in this article. In three examples, four types of measurement errors have been used to confirm the accuracy of the present method and compare the results with other methods. The stability of the present method has been investigated in all examples when the input data is contaminated with noise. Considering that in each example, the optimum value of parameter a is obtained, the results are stable in noise mode. The results in the examples also show the accuracy and advantage of the present method in comparison with the other method.

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Acknowledgements

We thank the anonymous reviewers for helpful comments, which lead to definite improvement in the manuscript.

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Authors and Affiliations

  1. Department of Applied Mathematics, Imam Khomeini International University, 34149-16818, Qazvin, Iran

    Jalal Hajishafieiha & Saeid Abbasbandy

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  1. Jalal Hajishafieiha
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  2. Saeid Abbasbandy
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Correspondence to Saeid Abbasbandy.

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Hajishafieiha, J., Abbasbandy, S. Numerical solution of two-dimensional inverse time-fractional diffusion problem with non-local boundary condition using a-polynomials. J. Appl. Math. Comput. 69, 1945–1965 (2023). https://doi.org/10.1007/s12190-022-01812-0

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