A Jacobi-Gauss-Lobatto collocation method for solving generalized Fitzhugh-Nagumo equation with time-dependent coefficients. (English) Zbl 1329.65234

Bhrawy, A. H.

Appl. Math. Comput. 222, 255-264 (2013).

Summary: In this paper, we propose a new Jacobi-Gauss-Lobatto collocation method for solving the generalized Fitzhugh-Nagumo equation. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. The proposed method has the advantage of obtaining the solution in terms of the Jacobi parameters \(\alpha\) and \(\beta\). In addition, the problem is reduced to a system of ordinary differential equations in time. This system can be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solution reveal that the obtained solution produces high accurate results. Numerical results show that the proposed method is of high accuracy and is efficient for solving the generalized Fitzhugh-Nagumo equation. Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
92C30	Physiology (general)

Keywords:

time-dependent Fitzhugh-Nagumo equation; generalized Fitzhugh-Nagumo equation; real Newell-Whitehead equation; collocation method; Jacobi-Gauss-Lobatto quadrature; implicit Runge-Kutta method