Journal of Applied Mathematics
Volume 2012 (2012), Article ID 796814, 12 pages
Research Article

Exponential Time Integration and Second-Order Difference Scheme for a Generalized Black-Scholes Equation

Institute of Mathematics, Zhejiang Wanli University, Zhejiang, Ningbo 315100, China

Received 20 September 2011; Revised 5 December 2011; Accepted 5 December 2011

Academic Editor: Kai Diethelm

Copyright © 2012 Zhongdi Cen 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.


We apply an exponential time integration scheme combined with a central difference scheme on a piecewise uniform mesh with respect to the spatial variable to evaluate a generalized Black-Scholes equation. We show that the scheme is second-order convergent for both time and spatial variables. It is proved that the scheme is unconditionally stable. Numerical results support the theoretical results.