Local radial basis function interpolation method to simulate 2D fractional-time convection-diffusion-reaction equations with error analysis. (English) Zbl 1370.65041

Shivanian, Elyas

Numer. Methods Partial Differ. Equations 33, No. 3, 974-994 (2017).

The meshless local radial point interpolation method has been successfully applied to the fractional-time convection-diffusion-reaction equation. The method is based on meshless methods and benefits from collocation techniques. With the help of thin plate splines, the point interpolation method is proposed to construct the basis function. A finite difference numerical scheme is developed for the fractional-time convection-diffusion-reaction equation. The stability and convergence of the numerical scheme are studied. Two examples, one for fractional sub-diffusion-convection and the other one for the sub-diffusion convection-reaction clearly demonstrate the applicability of the scheme. The error is within a reasonable limit. Some lemmas and theorems are also stated and proved.

Reviewer: K. N. Shukla (Gurgaon)

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K57	Reaction-diffusion equations
35R11	Fractional partial differential equations
65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

time-fractional derivatives; radial basis function; thin plate spline; meshless local radial point interpolation method; fractional subdiffusion-convection; fractional subdiffusion-convection-reaction; numerical examples; error bounds; collocation; fractional-time convection-diffusion-reaction equation; stability; convergence

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