A Haar wavelet quasilinearization approach for numerical simulation of Burgers' equation

In this paper, an efficient numerical scheme based on uniform Haar wavelets and the quasilinearization process is proposed for the numerical simulation of time dependent nonlinear Burgers' equation. The equation has great importance in many physical problems such as fluid dynamics, turbulence, sound waves in a viscous medium etc. The Haar wavelet basis permits to enlarge the class of functions used so far in the collocation framework. More accurate solutions are obtained by wavelet decomposition in the form of a multi-resolution analysis of the function which represents a solution of boundary value problems. The accuracy of the proposed method is demonstrated by three test problems. The numerical results are compared with existing numerical solutions found in the literature. The use of the uniform Haar wavelet is found to be accurate, simple, fast, flexible, convenient and has small computation costs.