Mixed-type discontinuous Galerkin approach for solving the generalized FitzHugh–Nagumo reaction–diffusion model - Singh, Satyvir (2022)
The generalized FitzHugh–Nagumo reaction–diffusion model has long been fascinating topic in the field of the mathematical and physics. This paper is aimed to present a mixed-type discontinuous Galerkin approach to solve the generalized FitzHugh–Nagumo reaction–diffusion model. An auxiliary variable is introduced in the governing equation for handling the higher-order term. The scaled Legendre polynomial functions are used for the spatial discretization. The numerical technique transforms the problem into a system of semi-discrete ordinary differential equation which is solved by an explicit three-stages, third-order SSP Runge-Kutta scheme. For verifying the accuracy and efficiency, the numerical scheme is tested on some different problems of generalized FitzHugh–Nagumo model with constant and time-dependent coefficients. The obtained results are very close to the exact solutions and better than those obtained by some other numerical schemes. This scheme plays as an alternative option for solving the nonlinear reaction–diffusion type equations.