Approximation of the Huxley equation with nonstandard nite-difference scheme

In this paper, an explicit exact finite difference scheme for the Huxley equation is presented based on the nonstandard finite-difference (NSFD) scheme. Afterwards, an NSFD scheme is proposed for the numerical solution of the Huxley equation. The positivity and boundedness of the scheme is discussed. It is shown through analysis that the proposed scheme is consistent, stable, and convergence. The numerical results obtained by the NSFD scheme is compared with the exact solution and some available methods, to verify the accuracy and efficiency of the NSFD scheme

Keywords:

The Huxley equation , nonstandard finite-difference scheme , Positivity and boundedness , consistency , stability , convergence