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A RBF-based differential quadrature method for solving two-dimensional variable-order time fractional advection-diffusion equation. (English) Zbl 1451.65131
Summary: Numerical simulation technique of two-dimensional variable-order time fractional advection-diffusion equation is developed in this paper using radial basis function-based differential quadrature method (RBF-DQ). To the best of the authors’ knowledge, this is the first application of this method to variable-order time fractional advection-diffusion equations. For the general case of irregular geometries, the meshless local form of RBF-DQ is used and the multiquadric type of radial basis functions is selected for the computations. This approach allows one to define a reconstruction of the local radial basis functions to treat accurately both the Dirichlet and Neumann boundary conditions on the irregular boundaries. The method is validated by the well documented test examples involving variable-order fractional modeling of air pollution. The numerical results demonstrate that the proposed method provides accurate solutions for two-dimensional variable-order time fractional advection-diffusion equations.

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
65D12 Numerical radial basis function approximation
Matlab; SU2
Full Text: DOI
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