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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:369

Article

Aldoghaither, Abeer¹  Laleg-Kirati, Taous-Meriem² 

[1] Dar Al Hekma Univ, Gen Educ Dept, Jeddah, Saudi Arabia

[2] King Abdullah Univ Sci & Technol, Math & Computat Sci & Engn Div, Thuwal, Saudi Arabia

关键词: Fractional partial differential equations;    Modulating functions;    Parameter estimation;    Newton algorithm;   

DOI  :  10.1016/j.cam.2019.112570

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free