TY - JOUR

T1 - A meshless technique based on the moving least squares shape functions for nonlinear fractal-fractional advection-diffusion equation

AU - Hosseininia, M.

AU - Heydari, M. H.

AU - Maalek Ghaini, F. M.

AU - Avazzadeh, Z.

N1 - Publisher Copyright:
© 2021

PY - 2021/6/1

Y1 - 2021/6/1

N2 - 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.

AB - 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.

KW - Fractal-fractional derivative

KW - Moving least squares shape functions

KW - Nonlinear fractal-fractional 2D advection-diffusion equation

UR - http://www.scopus.com/inward/record.url?scp=85103271505&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2021.03.003

DO - 10.1016/j.enganabound.2021.03.003

M3 - Article

AN - SCOPUS:85103271505

SN - 0955-7997

VL - 127

SP - 8

EP - 17

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

ER -