- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 156965, 10 pages
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.
- R. K. Gazizov and N. H. Ibragimov, “Lie symmetry analysis of differential equations in finance,” Nonlinear Dynamics, vol. 17, no. 4, pp. 387–407, 1998.
- C. A. Pooe, F. M. Mahomed, and C. Wafo Soh, “Invariant solutions of the Black-Scholes equation,” Mathematical & Computational Applications, vol. 8, no. 1–3, pp. 63–70, 2003.
- M. Craddock and E. Platen, “Symmetry group methods for fundamental solutions,” Journal of Differential Equations, vol. 207, no. 2, pp. 285–302, 2004.
- M. Craddock and K. A. Lennox, “Lie group symmetries as integral transforms of fundamental solutions,” Journal of Differential Equations, vol. 232, no. 2, pp. 652–674, 2007.
- M. Craddock and K. A. Lennox, “Lie symmetry methods for multi-dimensional parabolic PDEs and diffusions,” Journal of Differential Equations, vol. 252, no. 1, pp. 56–90, 2012.
- W. Sinkala, P. G. L. Leach, and J. G. O'Hara, “Invariance properties of a general bond-pricing equation,” Journal of Differential Equations, vol. 244, no. 11, pp. 2820–2835, 2008.
- J. Si, S. Chen, and P. Gong, “The FEM solution of valuation modal of TF convertible bonds,” Journal of Huazhong University of Science and Technology, vol. 32, pp. 101–103, 2004 (Chinese).
- H. Liu, J. Li, and L. Liu, “Lie group classifications and exact solutions for two variable-coefficient equations,” Applied Mathematics and Computation, vol. 215, no. 8, pp. 2927–2935, 2009.
- H. Liu, J. Li, and L. Liu, “Painlevé analysis, Lie symmetries, and exact solutions for the time-dependent coefficients Gardner equations,” Nonlinear Dynamics, vol. 59, no. 3, pp. 497–502, 2010.
- H. Liu, J. Li, and Q. Zhang, “Lie symmetry analysis and exact explicit solutions for general Burgers' equation,” Journal of Computational and Applied Mathematics, vol. 228, no. 1, pp. 1–9, 2009.
- H. Liu, J. Li, L. Liu, and Y. Wei, “Group classifications, optimal systems and exact solutions to the generalized Thomas equations,” Journal of Mathematical Analysis and Applications, vol. 383, no. 2, pp. 400–408, 2011.
- H. Liu, J. Li, and L. Liu, “Complete group classification and exact solutions to the generalized short pulse equation,” Studies in Applied Mathematics, vol. 129, no. 1, pp. 103–116, 2012.
- H. Liu and Y. Geng, “Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid,” Journal of Differential Equations, vol. 254, no. 5, pp. 2289–2303, 2013.
- P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1993.
- G. W. Bluman and S. C. Anco, Symmetry and Integration Methods for Differential Equations, vol. 154 of Applied Mathematical Sciences, Springer, New York, NY, USA, 2002.
- E. Pucci and G. Saccomandi, “Potential symmetries and solutions by reduction of partial differential equations,” Journal of Physics, vol. 26, no. 3, pp. 681–690, 1993.
- C. Qu and Q. Huang, “Symmetry reductions and exact solutions of the affine heat equation,” Journal of Mathematical Analysis and Applications, vol. 346, no. 2, pp. 521–530, 2008.
- T. Chaolu and P. Jing, “An algorithm for the complete symmetry classification of differential equations based on Wu's method,” Journal of Engineering Mathematics, vol. 66, no. 1–3, pp. 181–199, 2010.
- H. Liu and W. Li, “The exact analytic solutions of a nonlinear differential iterative equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 8, pp. 2466–2478, 2008.
- N. Asmar, Partial Differential Equations with Fourier Series and Boundary Value Problems, China Machine Press, Beijing, China, 2nd edition, 2005.