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

## Abstract

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.

- Authors:

- Vali-e-Asr University of Rafsanjan, Department of Mathematics, School of Mathematical Sciences (Iran, Islamic Republic of)
- Islamic Azad University, Department of Mathematics, Bojnourd Branch (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 22769343

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; COMPARATIVE EVALUATIONS; ERRORS; EXACT SOLUTIONS; NUMERICAL SOLUTION

### Citation Formats

```
Namjoo, Mehran, and Zibaei, Sadegh.
```*Numerical solutions of FitzHugh–Nagumo equation by exact finite-difference and NSFD schemes*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0406-9.

```
Namjoo, Mehran, & Zibaei, Sadegh.
```*Numerical solutions of FitzHugh–Nagumo equation by exact finite-difference and NSFD schemes*. United States. doi:10.1007/S40314-016-0406-9.

```
Namjoo, Mehran, and Zibaei, Sadegh. Tue .
"Numerical solutions of FitzHugh–Nagumo equation by exact finite-difference and NSFD schemes". United States. doi:10.1007/S40314-016-0406-9.
```

```
@article{osti_22769343,
```

title = {Numerical solutions of FitzHugh–Nagumo equation by exact finite-difference and NSFD schemes},

author = {Namjoo, Mehran and Zibaei, Sadegh},

abstractNote = {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.},

doi = {10.1007/S40314-016-0406-9},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}

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