Numerical solutions of FitzHugh-Nagumo equation by exact finite-difference and NSFD schemes

作者：Namjoo Mehran^*; Zibaei Sadegh

来源：COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37(2): 1395-1411.

DOI：10.1007/s40314-016-0406-9

• Exact finite-difference scheme
• The FitzHugh-Nagumo equation
• Nonstandard finite-difference scheme
• Boundedness
• Local truncation error

In this paper, numerical solution of the FitzHugh-Nagumo (FN) equation is presented based on the nonstandard finite-difference (NSFD) scheme. At first, two exact finite-difference schemes for FN equation are obtained. Moreover, two NSFD schemes are presented for this equation. The positivity, boundedness, and local truncation error of the schemes are discussed. The numerical results obtained by the NSFD schemes are compared with the exact solution and some available methods, to verify the accuracy and efficiency of the NSFD schemes.

• 出版日期2018-5