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Journal of Scientific Computing

Erschienen in:

01.05.2020

Regularization Technique for an Inverse Space-Fractional Backward Heat Conduction Problem

verfasst von: Milad Karimi, Fridoun Moradlou, Mojtaba Hajipour

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2020

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Abstract

This manuscript deals with a regularization technique for a generalized space-fractional backward heat conduction problem (BHCP) which is well-known to be extremely ill-posed. The presented technique is developed based on the Meyer wavelets in retrieving the solution of the presented space-fractional BHCP. Some sharp optimal estimates of the Hölder-Logarithmic type are theoretically derived by imposing an a-priori bound assumption via the Sobolev scale. The existence, uniqueness and stability of the considered problem are rigorously investigated. The asymptotic error estimates for both linear and non-linear problems are all the same. Finally, the performance of the proposed technique is demonstrated through one- and two-dimensional prototype examples that validate our theoretical analysis. Furthermore, comparative results verify that the proposed method is more effective than the other existing methods in the literature.

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Nächster Artikel An H2N2 Interpolation for Caputo Derivative with Order in (1, 2) and Its Application to Time-Fractional Wave Equations in More Than One Space Dimension

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Titel: Regularization Technique for an Inverse Space-Fractional Backward Heat Conduction Problem
verfasst von: Milad Karimi
Fridoun Moradlou
Mojtaba Hajipour
Publikationsdatum: 01.05.2020
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01211-2

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