Polynomial differential quadrature method for numerical solutions of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients

Abstract

In this paper, polynomial differential quadrature method (PDQM) is applied to find the numerical solution of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients in one dimensional space. The PDQM reduces the problem into a system of first order non-linear differential equations. Then, the obtained system is solved by optimal four-stage, order three strong stability-preserving time-stepping Runge–Kutta (SSP-RK43) scheme. The accuracy and efficiency of the proposed method are demonstrated by three test examples. The numerical results are shown in max absolute errors (L∞), root mean square errors (RMS) and relative errors (L2) forms. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions are very similar to the exact ones.

Keywords

• Generalized Fitzhugh–Nagumo equation
• Polynomial differential quadrature method
• Numerical solutions
• Runge–Kutta method