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Implicit radial point interpolation method for nonlinear space fractional advection-diffusion equations. (English) Zbl 1456.65091

Summary: This paper aims to employ the implicit radial point interpolation method, which is intrinsically meshless, for the numerical simulation of nonlinear space fractional advection-diffusion equations. The space fractional derivative is defined in the Caputo sense and calculated by the Gauss’s Jacobi quadrature formula. The accuracy and convergency of the proposed meshless method are demonstrated by several numerical examples with different regions and different nodal distributions. It is proved that the presented method is computational efficiency for modeling and simulation of nonlinear SFADEs.

MSC:

65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65D32 Numerical quadrature and cubature formulas
35R11 Fractional partial differential equations
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References:

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