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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 156965, 10 pages
http://dx.doi.org/10.1155/2013/156965
Research Article

Symmetry Analysis and Exact Solutions to the Space-Dependent Coefficient PDEs in Finance

1School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252059, China
2Department of Mathematics, Binzhou University, Binzhou, Shandong 256603, China

Received 20 June 2013; Accepted 25 August 2013

Academic Editor: Mariano Torrisi

Copyright © 2013 Hanze Liu. 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

The variable-coefficients partial differential equations (vc-PDEs) in finance are investigated by Lie symmetry analysis and the generalized power series method. All of the geometric vector fields of the equations are obtained; the symmetry reductions and exact solutions to the equations are presented, including the exponentiated solutions and the similarity solutions. Furthermore, the exact analytic solutions are provided by the transformation technique and generalized power series method, which has shown that the combination of Lie symmetry analysis and the generalized power series method is a feasible approach to dealing with exact solutions to the variable-coefficients PDEs.