Haar Wavelet Method for the Numerical Solution of Benjamin–Bona–Mahony Equations

Abstract

In this paper, we proposed an efficient numerical method based on uniform Haar wavelet for the numerical solutions oflinear and nonlinear Benjamin\u2013Bona\u2013Mahony (BBM) Equations. Such types of problems arise in various fields of science and engineering. In present study more accurate solutions have been obtained by Haar wavelet decomposition with multiresolution analysis. Three test problems are considered to check theefficiency and accuracy of the proposed method.An extensiveamount of error analysis has been carried out to obtain the convergence of the method.The numerical results are found in good agreement with exact and finite difference method (FDM), which shows that the solution using Haar wavelet method (HWM) is more effective and accurate and manageable for these equations.