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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749 . Open Access


Radial Basis Function Pseudospectral Method for Solving Standard Fitzhugh-Nagumo Equation

Radial Basis Function Pseudospectral Method for Solving Standard Fitzhugh-Nagumo Equation

Geeta Arora
Department of Mathematics, Lovely Professional University, Punjab, India.

Gurpreet Singh Bhatia
Department of Mathematics, Lovely Professional University, Punjab, India.

DOI https://doi.org/10.33889/IJMEMS.2020.5.6.110

Received on February 06, 2020
  ;
Accepted on August 21, 2020

Abstract

In this article, a pseudospectral approach based on radial basis functions is considered for the solution of the standard Fitzhugh-Nagumo equation. The proposed radial basis function pseudospectral approach is truly mesh free. The standard Fitzhugh-Nagumo equation is approximated into ordinary differential equations with the help of radial kernels. An ODE solver is applied to solve the resultant ODEs. Shape parameter which decides the shape of the radial basis function plays a significant role in the solution. A cross-validation technique which is the extension of the statistical approach leave-one-out-cross-validation is used to find the shape parameter value. The presented method is demonstrated with the help of numerical results which shows a good understanding with the exact solution. The stability of the proposed method is demonstrated with the help of the eigenvalues method numerically.

Keywords- FN equation, Radial basis function, Meshless.

Citation

Arora, G., & Bhatia, G. S. (2020). Radial Basis Function Pseudospectral Method for Solving Standard Fitzhugh-Nagumo Equation. International Journal of Mathematical, Engineering and Management Sciences, 5(6), 1488-1497. https://doi.org/10.33889/IJMEMS.2020.5.6.110.