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Journal of Applied Mathematics and Computing

Erschienen in:

16.11.2022 | Original Research

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

verfasst von: Jalal Hajishafieiha, Saeid Abbasbandy

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 2/2023

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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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Titel: Numerical solution of two-dimensional inverse time-fractional diffusion problem with non-local boundary condition using a-polynomials
verfasst von: Jalal Hajishafieiha
Saeid Abbasbandy
Publikationsdatum: 16.11.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 2/2023
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-022-01812-0

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