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

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.

### 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
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