A hybrid numerical scheme for the numerical solution of the Burgers’ equation

Abstract

In this article, a hybrid numerical scheme based on Euler implicit method, quasilinearization and uniform Haar wavelets has been developed for the numerical solutions of Burgers’ equation. Most of the numerical methods available in the literature fail to capture the physical behavior of the equations when viscosity ν→0. In Jiwari (2012), the author presented the numerical results up to ν=0.003 and the scheme failed for values smaller than ν=0.003. The main aim in the development of the present scheme is to overcome the drawback of the scheme developed in Jiwari (2012). Lastly, three test problems are chosen to check the accuracy of the proposed scheme. The approximated results are compared with existing numerical and exact solutions found in literature. The use of uniform Haar wavelet is found to be accurate, simple, fast, flexible, convenient and at small computation costs.