Numerical Solution of the Rosenau–Hyman Equation by the Extended Jacobi Wavelet Method

In this paper, we present a general operational matrix of integration for the extended Jacobi wavelet. Furthermore, we apply this framework to obtain an approximate solution of the nonlinear Rosenau–Hyman equation. The proposed method is based on a wavelet technique that leverages the properties of Jacobi polynomials to enhance computational accuracy. We perform a comparative analysis of the approximate solution for various parameter values to investigate its behavior and precision. In addition, we compute the absolute error, relative error, as well as the and errors for different parameter settings, thereby demonstrating the efficiency and reliability of the proposed method. Moreover, we prove some theorems regarding the convergence and error estimates of the method with respect to different norms.