- About this Journal
- Abstracting and Indexing
- 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 2012 (2012), Article ID 253890, 14 pages
Enhanced Multistage Differential Transform Method: Application to the Population Models
1Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea
2Ulsan National Institute of Science and Technology (UNIST), Ulsan Metropolitan City 689-798, Republic of Korea
Received 25 March 2012; Accepted 1 April 2012
Academic Editor: Shaher Momani
Copyright © 2012 Younghae Do and Bongsoo Jang. 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.
- F. Kangalgil and F. Ayaz, “Solitary wave solutions for the KdV and mKdV equations by differential transform method,” Chaos, Solitons and Fractals, vol. 41, no. 1, pp. 464–472, 2009.
- A. S. V. Ravi Kanth and K. Aruna, “Differential transform method for solving linear and non-linear systems of partial differential equations,” Physics Letters. A, vol. 372, no. 46, pp. 6896–6898, 2008.
- I. H. A. Hassan, “Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems,” Chaos, Solitons and Fractals, vol. 36, no. 1, pp. 53–65, 2008.
- F. Ayaz, “Solutions of the system of differential equations by differential transform method,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 547–567, 2004.
- I. H. A. Hassan, “Different applications for the differential transformation in the differential equations,” Applied Mathematics and Computation, vol. 129, no. 2-3, pp. 183–201, 2002.
- M. J. Jang, C. L. Chen, and Y. C. Liu, “Two-dimensional differential transform for partial differential equations,” Applied Mathematics and Computation, vol. 121, no. 2-3, pp. 261–270, 2001.
- B. Jang, “Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 224–230, 2009.
- B. Jang, “Solving linear and nonlinear initial value problems by the projected differential transform method,” Computer Physics Communications, vol. 181, no. 5, pp. 848–854, 2010.
- H. Koçak and A. Yıldırım, “An efficient algorithm for solving nonlinear age-structured population models by combining homotopy perturbation and Padé techniques,” International Journal of Computer Mathematics, vol. 88, no. 3, pp. 491–500, 2011.
- A. Yildirim and Y. Cherruault, “Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method,” Kybernetes, vol. 38, no. 9, pp. 1566–1575, 2009.
- A. Gökdoğan, M. Merdan, and A. Yildirim, “A multistage differential transformation method for approximate solution of Hantavirus infection model,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 1–8, 2012.
- A. Gökdoǧan, M. Merdan, and A. Yildirim, “Adaptive multi-step differential transformation method to solving nonlinear differential equations,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 761–769, 2012.
- Z. M. Odibat, C. Bertelle, M. A. Aziz-Alaoui, and G. H. E. Duchamp, “A multi-step differential transform method and application to non-chaotic or chaotic systems,” Computers & Mathematics with Applications, vol. 59, no. 4, pp. 1462–1472, 2010.
- V. S. Ertürk, Z. M. Odibat, and S. Momani, “An approximate solution of a fractional order differential equation model of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 996–1002, 2011.
- V. S. Erturk, G. Zaman, and S. Momani, “A numeric-analytic method for approximating a giving up smoking model containing fractional derivatives,” Computers & Mathematics with Applications. In press.
- V.S. Erturk, G. Zaman, and S. Momani, “Application of multi-step differential transform method for the analytical and numerical solutions of the density dependent Nagumo telegraph equation,” Romanian Journal of Physics. In press.
- S. M. Goh, M. S. M. Noorani, and I. Hashim, “Prescribing a multistage analytical method to a prey-predator dynamical system,” Physics Letters, Section A, vol. 373, no. 1, pp. 107–110, 2008.
- S. M. Moghadas, M. E. Alexander, and B. D. Corbett, “A non-standard numerical scheme for a generalized Gause-type predator-prey model,” Physica D, vol. 188, no. 1-2, pp. 134–151, 2004.
- B. Batiha, M. S. M. Noorani, I. Hashim, and E. S. Ismail, “The multistage variational iteration method for a class of nonlinear system of ODEs,” Physica Scripta, vol. 76, no. 4, pp. 388–392, 2007.
- B. Batiha, M. S. M. Noorani, and I. Hashim, “Variational iteration method for solving multispecies Lotka-Volterra equations,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 903–909, 2007.