The solution of the prey and predator problem by differential transformation method

Authors

  • Belal Batiha Higher Colleges of Technology (HCT), Abu Dhabi Men's College, United Arab Emirates (UAE)

DOI:

https://doi.org/10.14419/ijbas.v4i1.4034

Keywords:

Differential transformation method, Taylor's series expansion, prey and predator problem, Adomian decomposition method.

Abstract

The problem of prey and predator is solved by the dierential transformation method (DTM). Numerical comparisons with Adomian decomposition method (ADM) and power series method are presented.

References

  1. J. Biazar, R. Montazeri, A computational method for solution of the prey and predator problem, Applied Mathematics and Computation 163 (2005) 841-847. http://dx.doi.org/10.1016/j.amc.2004.05.001
  2. J. Biazar, M. Ilie, A. Khoshkenar, A new approach to the solution of the prey and predator problem and comparison of the results with the Adomian method, Applied Mathematics and Computation 171 (2005) 486-491. http://dx.doi.org/10.1016/j.amc.2005.01.040
  3. M. Rafei, H. Daniali, D.D. Ganji, Variational iteration method for solving the epidemic model and the prey and predator problem, Applied Mathematics and Computation, 186 (2) (2007) 1701-1709. http://dx.doi.org/10.1016/j.amc.2006.08.077
  4. S.M. Goh, M.S.M. Noorani, I. Hashim, Prescribing a multistage analytical method to a preypredator dynamical system, Physics Letters A, 373 (2008) 107-110. http://dx.doi.org/10.1016/j.physleta.2008.11.009
  5. J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986. (in Chinese).
  6. C.L. Chen, Y.C. Liu, Differential transformation technique for steady nonlinear heat conduction problems, Applied Mathematics and Computation 95 (1998) 155-164. http://dx.doi.org/10.1016/S0096-3003(97)10096-0
  7. C.L. Chen, Y.C. Liu, Solution of two point boundary value problems using the differential transformation method, Journal of Optimization Theory and Applications 99 (1998) 23-35. http://dx.doi.org/10.1023/A:1021791909142
  8. C.L. Chen, S.H. Lin, C.K. Chen, Application of Taylor transformation to nonlinear predictive control problem, Applied Mathematical Modeling 20 (1996) 699-710. http://dx.doi.org/10.1016/0307-904X(96)00050-9
  9. C.K. Chen, S.H. Ho, Application of differential transformation to eigenvalue problems, Applied Mathematics and Computation 79 (1996) 173-188. http://dx.doi.org/10.1016/0096-3003(95)00253-7
  10. C. L. Chen, Y. C. Liu. Solution of two point boundary value problems using the differential transformation method. JOpt Theory Appl., 99(1998):23-35. http://dx.doi.org/10.1023/A:1021791909142
  11. F. Ayaz. Applications of differential transform method to differential-algebraic equations. Applied Mathematics and Computation, 152(2004):649-657. http://dx.doi.org/10.1016/S0096-3003(03)00581-2
  12. F. Kangalgil, F. Ayaz. Solitary wave solutions for the KdV and mKdV equations by differential transform method. Chaos, Solitons and Fractals, 41(2009)(1):464-472.
  13. S. V. Ravi Kanth, K. Aruna. Two-dimensional differential transform method for solving linear and non-linear Schrodinger equations. Chaos, Solitons and Fractals, 41(2009)(5):2277-2281.
  14. A. Arikoglu, I. Ozkol. Solution of fractional differential equations by using differential transform method. Chaos, Solitons and Fractals, 34(2007):1473-1481. http://dx.doi.org/10.1016/j.chaos.2006.09.004
  15. J. Biazar, M. Eslami, Differential Transform Method for Quadratic Riccati Differential Equation, International Journal of Nonlinear Science, 9 (4) (2010) 444-447.
  16. M.J. Jang, C.L. Chen, Y.C. Liy, On solving the initial value problems using the differential transformation method, Applied Mathematics and Computation 115 (2000) 145-160. http://dx.doi.org/10.1016/S0096-3003(99)00137-X
  17. I.H. A. Hassan, Differential transformation technique for solving higher-order initial value problems, Applied Mathematics and Computation 154 (2004) 299-311 http://dx.doi.org/10.1016/S0096-3003(03)00708-2
  18. S-H. Chang, I-L. Chang, A new algorithm for calculating one-dimensional differential transform of nonlinear functions, Applied Mathematics and Computation 195 (2008) 799-808. http://dx.doi.org/10.1016/j.amc.2007.05.026
  19. S. Schnell,C. Mendoza, Closed form solution for time-dependent enzyme kinetics. J. Theor. Biol. 187 (1997) 207-212. http://dx.doi.org/10.1006/jtbi.1997.0425
  20. AK. Sen, An application of the Adomian decomposition method to the transient behavior of a model biochemical reaction. J. Math. Anal. Appl. 131 (1988) 232-245. http://dx.doi.org/10.1016/0022-247X(88)90202-8
  21. I. Hashim, M.S.H. Chowdhury b, S. Mawa, On multistage homotopy-perturbation method applied to nonlinear biochemical reaction model, Chaos, Solitons and Fractals 36 (2008) 823-827. http://dx.doi.org/10.1016/j.chaos.2007.09.009

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Published

2014-12-16

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