Solving scalar reaction diffusion equations with cubic non-linearity having time-dependent coefficients by the wavelet method of lines

Abstract

This paper aims to conduct the numerical solutions of the scalar reaction diffusion model with cubic non-linearity having constant and time-dependent coefficients. The proposed method is hybrid in nature in which Haar wavelets are used to approximate the spatial derivatives and the Runge-Kutta (RK) routines are used to solve the resultant system of ordinary differential equations. We illustrate the applicability and efficiency of the proposed method by computing $ L_2 $, $ L_{\infty} $, and $ L_{rms} $ error estimates for various test models. The numerical accuracy and stability of the Haar wavelet-based method of lines for solving the scaler reaction-diffusion model provides further insight into the use of this scheme for model equations across various disciplines.