Approximation of the Huxley equation with nonstandard finite-difference scheme

Document Type : Research Article

Authors

• M. Namjoo
• S. Zibaei

Department of Mathematics, Vali{e{Asr University of Rafsanjan, Rafsanjan, Iran.

10.22067/ijnao.v9i1.61735

Abstract

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

20.1001.1.24236977.2019.9.1.2.5

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