Numerical solution and stability analysis of huxley equation

الملخص AR

The numerical solution of Huxley equation by the use of two finite difference methods is done.

The first one is the explicit scheme and the second one is the Crank-Nicholson scheme.

The comparison between the two methods showed that the explicit scheme is easier and has faster convergence while the Crank-Nicholson scheme is more accurate.

In addition, the stability analysis using Fourier (von Neumann) method of two schemes is investigated.

The resulting analysis showed that the first scheme is conditionally stable if, ( ) ( )2 2 4 , 2 4 2 a x r a t t x - D D D £ - D £ b b and the second scheme is unconditionally stable.