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

Purpose: This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a permeable wall in the presence of a magnetic field.Design/methodology/approach: Using the Lie group approach, the Lie algebra of infinitesimal generators of equivalence transformations is constructed for the equation under consideration. Using these suitable similarity transformations, the governing partial differential equations are reduced to linear and nonlinear ordinary differential equations (ODEs). Further, Haar wavelet approach is applied to the reduced ODE under the subalgebra 4.1 for constructing numerical solutions of the flow problem.Findings: A new type of solutions was obtained of the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis.Originality/value: To find a solution for the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis is a new approach for fluid problems.