Error analysis and numerical solution of Burgers–Huxley equation using 3-scale Haar wavelets

In this article, we develop an efficient and accurate numerical scheme based on the Crank–Nicolson finite difference method and Haar wavelet analysis to evaluate the numerical solution of the Burgers–Huxley equation. The present method is extended form of Haar wavelet 2D scaling which shows that it is reliable for solving nonlinear partial differential equations. The numerical results are more accurate than other existing methods available in the literature and very close to the exact solution. The Haar basis function is generated from multi-resolution analysis and used to evaluate fast and accurate approximate solutions on the collocation points. The convergence of the proposed method is demonstrated by its error analysis. We compared numerical solutions with the exact solutions and solutions available in the literature. The proposed method is found to be straight forward, accurate with small computational cost and can be easily implemented in mathematical software MATLAB.