Numerical Solutions of Huxley Equation By Haar Wavelet Method Ö

Numerical Solutions of Huxley Equation By Haar Wavelet Method
Ö. Oruç, F. Bulut and Alaattin Esen
alaattin.esen@inönü.edu.tr
İnönü University, Malatya
In this paper, we investigate the numerical solutions of nonlinear Huxley equation
with the help of Haar Wavelet (HW) method. The proposed method has been tested for
solutions of the problem with various time steps. Obtained numerical results are compared
with exact ones and Danafs' results who used collocation-based method using cubic B-spline
to solve this equation, obtained results have the higher accuracy with respect to spline
collocation method. Computer simulations show that the proposed method is computationally
cheap, fast, reliable and quite good even in the case of small number of grid points. Also the
calculated numerical solutions are drawn graphically.
References
Talaat S. El Danaf, (2011) "Efficient and accurate numerical treatment of Huxley equation",
International Journal of Numerical Methods forHeat & Fluid Flow, Vol. 21 Iss: 3, pp.282 –
292.
I. Çelik, Haar wavelet approximation for magnetohydrodynamic flow equations, Applied
Mathematical Modelling 37 (2013) 3894–3902.
U. Lepik, Numerical solution of differential equations using Haar wavelets, Math. Comput.
Simul. 68 (2005) 127–143.
R. Jiwari, A Haar wavelet quasilinearization approach for numerical simulation of Burgers’
equation, Computer Physics Communications 183 (2012) 2413–2423.

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