The Richtmyer type nonstandard finite difference scheme for numerical solutions of a nonlinear equation

The Burger‒Huxley equation as a well-known nonlinear physical model is studied numerically in the present paper.In this respect, the nonstandard finite difference (NSFD) scheme in company with the Richtmyer’s (۳, ۱, ۱) implicitformula is formally adopted to accomplish this goal. Moreover, the stability, convergence, and consistency analysesof nonstandard finite difference scheme are investigated systematically. Several case studies with comparisons areprovided, confirming that the current numerical scheme is capable of resulting in highly accurate approximations.

Keywords:

Burger‒Huxley equation , Nonstandard finite difference scheme , Richtmyer’s (۳ , ۱ , ۱) implicit formula , Consistency , Convergence , Stability