Abstract
The Fitzhugh-Naguno equation is one of the most popular and attractive equation in real life. This equation is applicable in many different areas of physics, biology, population genetics and applied sciences to mention a few. In this paper, we design and analyze a coupled scheme consisting of the non-standard finite difference and the Galerkin methods in both time and space variables respectively. We show analytically by the use of the Galerkin method and the compactness theorem that the solution of this equation exists uniquely in appropriate spaces with the parameter α that determines the main dynamics of the equation, under controlled. We further show numerically that the above scheme is stable and converge optimally in specified norms with its numerical solution replicating the qualitative properties of the exact solution. We finally present numerical experiments with the help of an example and a careful choice of α to validate the theoretical results.
| Original language | English |
|---|---|
| Pages (from-to) | 1983-2005 |
| Number of pages | 23 |
| Journal | Journal of Applied Analysis and Computation |
| Volume | 13 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2023 |
| Externally published | Yes |
Keywords
- Fitzhugh-Nagumo equation
- Galerkin and compactness methods
- non-standard finite difference
- stability and optimal rate of convergence