Turing models in the biological pattern formation through spectral meshless radial point interpolation approach

  • Elyas ShivanianEmail author
  • Ahmad Jafarabadi
Original Article


In the present paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the solution of pattern formation in nonlinear reaction diffusion systems. Firstly, we obtain a time discrete scheme by approximating the time derivative via a finite difference formula, then we use the SMRPI approach to approximate the spatial derivatives. This method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of SMRPI. In the current work, to eliminate the nonlinearity, a simple predictor–corrector (P–C) scheme is performed. The effect of parameters and conditions are studied by considering the well-known Schnakenberg model.


Turing systems Schnakenberg model Spectral meshless radial point interpolation (SMRPI) method Radial basis function Finite difference method 



The authors are grateful to the reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper. The authors also acknowledge financial support from the Imam Khomeini International University project IKIU-11829.


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsImam Khomeini International UniversityQazvinIran

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