Efficient and accurate numerical treatment of Huxley equation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 19 April 2011
Abstract
Purpose
The purpose of this paper is to demonstrate how numerical solutions of the nonlinear Huxley equation are obtained by collocation‐based method using cubic B‐spline over finite elements.
Design/methodology/approach
For the numerical procedure, time derivative is discretized using usual finite difference scheme. Solution and its principal derivatives over the subintervals are approximated by the combination of the cubic B‐spline and unknown element parameters.
Findings
The numerical results are found to be in good agreement with the exact solution. Also the method is very accurate and conditionally stable; the results are very accurate at a small h (discretization) of x so this method can be applied for any nonlinear partial differential equations.
Originality/value
The paper demonstrates how numerical solutions of the nonlinear Huxley equation are obtained by collocation‐based method using cubic B‐spline over finite elements.
Keywords
Citation
El Danaf, T.S. (2011), "Efficient and accurate numerical treatment of Huxley equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 3, pp. 282-292. https://doi.org/10.1108/09615531111108468
Publisher
:Emerald Group Publishing Limited
Copyright © 2011, Emerald Group Publishing Limited