Journal of Mathematical Chemistry

, Volume 51, Issue 9, pp 2432–2454

Two reliable wavelet methods to Fitzhugh–Nagumo (FN) and fractional FN equations

Original Paper

DOI: 10.1007/s10910-013-0220-1

Cite this article as:
Hariharan, G. & Rajaraman, R. J Math Chem (2013) 51: 2432. doi:10.1007/s10910-013-0220-1

Abstract

Fractional reaction–diffusion equations serve as more relevant models for studying complex patterns in several fields of nonlinear sciences. In this paper, we have developed the wavelet methods to find the approximate solutions for the Fitzhugh–Nagumo (FN) and fractional FN equations. The proposed method techniques provide the solutions in rapid convergence series with computable terms. To the best of our knowledge, until now there is no rigorous wavelet solutions have been reported for the FN and fractional FN equations arising in gene propagation and model. With the help of Laplace operator and Legendre wavelets operational matrices, the FN equation is converted into an algebraic system. Finally, we have given some numerical examples to demonstrate the validity and applicability of the wavelet methods. The power of the manageable method is confirmed. Moreover, the use of the wavelet methods is found to be accurate, efficient, simple, low computation costs and computationally attractive.

Keywords

Fitzhugh–Nagumo equationsFractional FN equationHaar waveletsLaplace transform methodLegendre wavelets Operational matricesHomotopy analysis method

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematics, School of Humanities and SciencesSASTRA UniversityThanjavurIndia