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An efficient numerical method for the solution of 2D variable order time fractional mobile–immobile advection–dispersion model
Author(s) -
Saffarian Marziyeh,
Mohebbi Akbar
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7158
Subject(s) - mathematics , discretization , legendre polynomials , stability (learning theory) , variable (mathematics) , convergence (economics) , order of accuracy , advection , mathematical analysis , convection–diffusion equation , numerical analysis , partial differential equation , numerical stability , physics , machine learning , computer science , economics , thermodynamics , economic growth
In the literature, there are a few efficient numerical methods with stability and convergence analysis for the solution of variable order fractional partial differential equations in higher dimensions. In this work, we propose an efficient numerical method for the solution of two‐dimensional variable order time fractional mobile–immobile advection–dispersion model with spatially variable convection coefficient. At first, we discretize the time derivatives with a second‐order scheme. Then, we apply the Legendre spectral element method in spatial directions and obtain the fully discrete scheme. We prove that the semi‐discrete scheme is unconditionally stable and present an error estimate for the fully discrete scheme. The numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.