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    Parameter and differentiation order estimation for a two dimensional fractional partial differential equation

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    Embargo End Date:
    2021-11-06
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    Type
    Article
    Authors
    Aldoghaither, Abeer
    Laleg-Kirati, Taous-Meriem cc
    KAUST Department
    Electrical Engineering Program
    Computational Bioscience Research Center (CBRC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-11-06
    Online Publication Date
    2019-11-06
    Print Publication Date
    2020-05
    Permanent link to this record
    http://hdl.handle.net/10754/659977
    
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    Abstract
    This paper deals with the estimation of coefficients and differentiation orders for two-dimensional fractional partial differential equations. Recently, a hybrid method based on modulating functions has been proposed by the authors to estimate the coefficients and a differentiation order for a one dimensional fractional advection dispersion equation in Aldoghaither et al. (2015). We propose to extend this method to the two-dimensional case. First, the coefficients are estimated using a modulating functions method, where the problem is transferred into solving a system of algebraic equations. Then, the modulating functions method combined with a Newton algorithm is proposed to estimate the coefficients and the differentiation orders simultaneously. Numerical example is presented with noisy measurements to show the effectiveness and the robustness of the method.
    Citation
    Aldoghaither, A., & Laleg-Kirati, T.-M. (2019). Parameter and differentiation order estimation for a two dimensional fractional partial differential equation. Journal of Computational and Applied Mathematics. doi:10.1016/j.cam.2019.112570
    Publisher
    Elsevier BV
    Journal
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2019.112570
    Additional Links
    https://linkinghub.elsevier.com/retrieve/pii/S0377042719305758
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cam.2019.112570
    Scopus Count
    Collections
    Articles; Electrical Engineering Program; Computational Bioscience Research Center (CBRC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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