Numerical solution of unperturbed and general perturbed Newell–Whitehead–Segel equation by the local discontinuous Galerkin method

Abstract

This paper investigates numerical solutions for the unperturbed and general perturbed Newell–Whitehead–Segel-type equations with the help of the local discontinuous Galerkin method. The stability analysis and error estimations of the proposed local discontinuous Galerkin algorithm are extensively examined. First, the spatial variables are discretized to provide a semidiscrete method of lines scheme. This generates an ordinary differential equation system in the temporal variable, which is subsequently solved using the total variation diminishing Runge–Kutta method of higher order. The generated numerical results are compared to the exact results and a few other existing numerical methods via various tables and figures to illustrate the efficiency and accuracy of the proposed method. The numerical results show that the proposed method is an effective numerical scheme for solving the Newell–Whitehead–Segel equation since the solutions obtained using the local discontinuous Galerkin method are highly close to the exact solutions with significantly less error.