Parameter and differentiation order estimation for a two dimensional fractional partial differential equation
Type
ArticleKAUST Department
Electrical Engineering ProgramComputational Bioscience Research Center (CBRC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2019-11-06Online Publication Date
2019-11-06Print Publication Date
2020-05Permanent link to this record
http://hdl.handle.net/10754/659977
Metadata
Show full item recordAbstract
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.2019.112570Publisher
Elsevier BVAdditional Links
https://linkinghub.elsevier.com/retrieve/pii/S0377042719305758ae974a485f413a2113503eed53cd6c53
10.1016/j.cam.2019.112570