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

摘要

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 O(k~2 + h~3)andO(1/M) 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.