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Local radial basis function interpolation method to simulate 2D fractional‐time convection‐diffusion‐reaction equations with error analysis
Author(s) -
Shivanian Elyas
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22135
Subject(s) - regularized meshless method , collocation method , radial basis function , mathematics , meshfree methods , orthogonal collocation , collocation (remote sensing) , interpolation (computer graphics) , partial differential equation , finite element method , basis function , galerkin method , singular boundary method , convergence (economics) , mathematical analysis , differential equation , computer science , ordinary differential equation , boundary element method , artificial neural network , animation , physics , computer graphics (images) , machine learning , economic growth , economics , thermodynamics
In this article, a kind of meshless local radial point interpolation (MLRPI) method is proposed to two‐dimensional fractional‐time convection‐diffusion‐reaction equations and satisfactory agreements are archived. This method is based on meshless methods and benefits from collocation ideas but it does not belong to the traditional global meshless collocation methods. In MLRPI method, it does not need any kind of integration locally or globally over small quadrature domains which is essential in the finite element method and those meshless methods based on Galerkin weak form. Also, it is not needed to determine shape parameter which plays important role in collocation method based on the radial basis functions (Kansa's method). Therefore, computational costs of this kind of MLRPI method is less expensive. The stability and convergence of this meshless approach are discussed and theoretically proven. It is proved that the present meshless formulation is very effective for modeling and simulation of fractional differential equations. Furthermore, the numerical studies on sensitivity analysis and convergence analysis show the stability and reliable rates of convergence. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 974–994, 2017