A multi-resolution hybrid Haar wavelet collocation method for solving nonlinear partial differential equations

This study focuses on approximation of several types of partial differential equations with different orders (including diffusion equation, Fisher equation, Atangana-Baleanu Burger’s equation and Korteweg-de Vries (KdV) equation). A multi-resolution (MR) based hybrid Haar wavelet collocation method (hHWCM) is proposed to approximate the exact solutions of discussed equations. The proposed method (hHWCM) is constructed on the basis of Euler’s formula (finite difference method (FDM)) and collocation procedure of Haar wavelet (HW) having multi-resolution characteristics. The algorithm of hHWCM is formulated using MATLAB coding. The nonlinear PDEs are linearized using Quasi Newton’s Technique 1 , whereas time discretization is performed using FDM and space discretization is obtained by HWCM. A comparative analysis between exact and approximate solutions is attained and stability of the proposed method is discussed. Moreover, the maximum absolute errors (MAEs) and experimental rate of convergence (ERoC) are calculated. The evaluations are displayed by means of figures and tables that indicate a good compatibility between the two solutions.