Journal
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
Volume 56, Issue -, Pages 129-144Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2015.02.005
Keywords
Keller-Segel model; Nonlinear equation; Kansa's approach; Radial basis functions (RBFs); Local collocation meshless method; Patlak-Keller-Segel chemotaxis model
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In this paper local radial basis functions (LRBFs) collocation method is proposed for solving the (Patlak-) Keller-Segel model. We use the Crank-Nicolson difference scheme for the time derivative to obtain a finite difference scheme with respect to the time variable for the Keller-Segel model. Then we use the local radial basis functions (LRBFs) collocation method to approximate the spatial derivative. We obtain the numerical results for the mentioned model. As we know, recently some approaches presented for preventing the blow up of the cell density. In the current paper we use the multiquadric (MQ) radial basis function. The aim of this paper is to show that the meshless methods based on the local RBFs collocation approach are also suitable for solving models that have the blow up of the cell density. Also, six test problems are given that show the acceptable accuracy and efficiency of the proposed schemes. (C) 2015 Elsevier Ltd. All rights reserved.
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