A numerical solution of the Burgers’ equation using a Crank-Nicolson exponential finite difference method
Abstract
This paper presents a new technique of forming improved exponential finite difference solution of Burgers’ equation. The technique is called Crank-Nicolson exponential finite difference method for the solution of Burgers’ equation. Since the equation is nonlinear the scheme leads to a system of nonlinear equations. At each time-step Newton’s method is used to solve this nonlinear system. The results are compared with exact values clearly show that results obtained using the method is precise and reliable.
Copyright © 2014 Bilge Inan, Ahmet Refik Bahadir. 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.
Cite this article
B. Inan, A. R. Bahadir, A numerical solution of the Burgers’ equation using a Crank-Nicolson exponential finite difference method, J. Math. Comput. Sci. 4 (2014), 849–860.
BibTeX
@article{Inan2014,
author = {Inan, Bilge and Bahadir, Ahmet Refik},
title = {A numerical solution of the Burgers’ equation using a Crank-Nicolson exponential finite difference method},
journal = {J. Math. Comput. Sci.},
volume = {4},
year = {2014},
pages = {849--860},
doi = {}
}