Explicit nonstandard finite difference discretisation of FitzHugh-Nagumo equations


  • Rao Appadu University of Pretoria
  • Michael Chapwanya University of Pretoria
  • Ayodeji Jejeniwa*
  • Jean Lubuma


In this work, we consider numerical solutions of the FitzHugh-Nagumo reaction diffusion system of equations describing the propagation of electrical signals in nerve axons. The system consists of two coupled equations: a nonlinear partial differential equation and a linear ordinary differential equation. We begin with a review of the qualitative properties of the system and the sub equations. This is followed by a systematic derivation of three explicit nonstandard finite difference schemes in the limit of fast extinction and slow recovery. A qualitative study of the schemes together with the error analysis is presented. Numerical simulations are given to support the theoretical results and verify the efficiency of the proposed schemes.






Conference Contributions