A meshless technique based on the moving least squares shape functions for nonlinear fractal-fractional advection-diffusion equation. (1st June 2021)

• Record Type: Journal Article
• Authors: Hosseininia, M.; Heydari, M.H.; Maalek Ghaini, F.M.; Avazzadeh, Z.
• Is Part Of: Engineering analysis with boundary elements. Volume 127(2021)
• Page Start: 8
• Page End: 17
• Publication Date: 2021-06-01
• Subjects: Moving least squares shape functions -- Fractal-fractional derivative -- Nonlinear fractal-fractional 2D advection-diffusion equation; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.03.003
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: This paper introduces a fractal-fractional version of the nonlinear 2D advection-diffusion equation and proposes a meshless method based on the moving least squares shape functions for its numerical solution. The fractal-fractional derivative in the Atangana-Riemann-Liouville is considered to define this equation. The proposed method includes the following steps: We first approximate the fractal-fractional derivative using the finite differences method and derive a recursive algorithm by applying the θ -weighted method. Next, using the moving least squares shape functions, we expand the solution of the problem and its corresponding partial derivatives and substitute them into the recurrence formula. Finally, in accordance with the previous step, we obtain a linear system of algebraic equations which must be solved at each time step. The validity and accuracy of the method are investigated by solving some numerical examples.