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 ( L 2 ) 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.