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The Scientific World Journal
Volume 2014 (2014), Article ID 780269, 13 pages
http://dx.doi.org/10.1155/2014/780269
Research Article

Two Different Methods for Numerical Solution of the Modified Burgers’ Equation

1Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University, 50300 Nevsehir, Turkey
2Department of Mathematics, Faculty of Science and Art, Inonu University, 44280 Malatya, Turkey

Received 23 January 2014; Accepted 23 February 2014; Published 3 April 2014

Academic Editors: D. Baleanu and H. Jafari

Copyright © 2014 Seydi Battal Gazi Karakoç et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A numerical solution of the modified Burgers’ equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing and error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM.