Applications of two numerical methods for solving inverse Benjamin–Bona–Mahony–Burgers equation

Abstract

In this paper, two numerical techniques are presented to solve the nonlinear inverse generalized Benjamin–Bona–Mahony–Burgers equation using noisy data. These two methods are the quartic B-spline and Haar wavelet methods combined with the Tikhonov regularization method. We show that the convergence rate of the proposed methods is $$\textit{O}(k^2+h^3)$$ and $$\textit{O}\left( \frac{1}{M}\right) $$ for the quartic B-spline and Haar wavelet method, respectively. In fact, this work considers a comparative study between quartic B-spline and Haar wavelet methods to solve some nonlinear inverse problems. Results show that an excellent estimation of the unknown functions of the nonlinear inverse problem has been obtained.