Efficient and accurate numerical treatment of Huxley equation

Efficient and accurate numerical treatment of Huxley equation 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

Efficient and accurate numerical treatment of Huxley equation

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Publisher
Emerald Publishing
Copyright
Copyright © 2011 Emerald Group Publishing Limited. All rights reserved.
ISSN
0961-5539
DOI
10.1108/09615531111108468
Publisher site
See Article on Publisher Site

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.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Apr 19, 2011

Keywords: Numerical analysis; Linear structure equation modeling; Finite element analysis

References

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