The modified algorithm for the differential transform method to solution of Genesio systems

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 1, 2012, Pages 45-51

  Gökdoĝan, Ahmet ^a   Merdan, Mehmet ^a   Yildirim, Ahmet ^b  

^a GUMUSHANE UNIVERSITY   (Turkey)

^b EGE UNIVERSITY   (Turkey)

Author keywords

Genesio systems; Pad approximant; The differential transform method

Indexed keywords

APPROXIMANTS; APPROXIMATE ANALYTICAL SOLUTIONS; CHAOTICS; CONVERGENCE RATES; GENESIO SYSTEMS; INVERSE LAPLACE TRANSFORM; MODIFIED ALGORITHMS; PADÉ APPROXIMANT; THE DIFFERENTIAL TRANSFORM METHOD;

LAPLACE TRANSFORMS;

EID: 79961027582     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.03.039     Document Type: Article

References (44)

1. J.K. Zhou, Differential Transformation and its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China.
2. Pukhov G.E. Computational structure for solving differential equations by Taylor transformations. Cybernt Syst Anal 1978, 14(3):383-390.
3. Baker G.A. Essentials of Padé Approximants 1975, Academic Press, London.
4. Chang S.H., Chang I.L. A new algorithm for calculating one-dimensional differential transform of nonlinear functions. Appl Math Comput 2008, 195:799-808.
5. Jordan D.W., Smith P. Nonlinear Ordinary Differential Equations 1999, Oxford University Press.
6. Ruan J., Lu Z. A modified algorithm for the Adomian decomposition method with applications to Genesiosystems. Math Comput Model 2007, 46:1214-1224.
7. Ho Shing S.H., Chen C.K. Analysis of general elastically end restrained non-uniform beams using differential transform. Appl Math Model 1998, 22:219-234.
8. Chen C.K., Ho S.H. Transverse vibration of a rotating twisted Timoshenko beam under axial loading using differential transform. Int J Mech Sci 1999, 41:1339-1356.
9. Jang M.J., Chen C.L., Liy Y.C. On solving the initial-value problems using the differential transformation method. Appl Math Comput 2000, 115:145-160.
10. Köksal M., Herdem S. Analysis of nonlinear circuits by using differential Taylor transform. Comput Electr Eng 2002, 28:513-525.
11. Ravi A.S.V.K., Aruna K. Solution of singular two-point boundary value problems using differential transformation method. Phys Lett A 2008, 372:4671-4673.
12. Ebaid A.E.H. Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method. Commun Nonlinear Sci Numer Simul 2010, 15:1921-1927.
13. Ayaz F. Solutions of the system of differential equations by differential transform Method. Appl Math Comput 2004, 147:547-567.
14. Chang S.H., Chang I.L. A new algorithm for calculating one-dimensional differential transform of nonlinear functions. Appl Math Comput 2008, 195:799-808.
15. Ravi A.S.V.K., Aruna K. Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations. Chaos Solitons Fract 2009, 41:2277-2281.
16. Ravi A.S.V.K., Aruna K. Differential transform method for solving the linear and nonlinear Klein-Gordon equation. Comput Phys Commun 2009, 180:708-711.
17. Venkatarangan S.N., Rajakshmi K. A modification of Adomian's solution for nonlinear oscillatory systems. Comput Math Appl 1995, 29:67-73.
18. Jiao Y.C., Yamamoto Y., Dang C., Hao Y. An after treatment technique for improving the accuracy of Adomian's decomposition method. Comput Math Appl 2002, 43:783-798.
19. El-Shahed M. Application of differential transform method to non-linear oscillatory systems. Commun Nonlinear Sci Numer Simul 2008, 13:1714-1720.
20. Chen C.L., Liu Y.C. Solution of two point boundary value problems using the differential transformation method. J Opt Theory Appl 1998, 99:23-35.
21. Jang M.J., Chen C.L., Liu Y.C. Two-dimensional differential transform for partial differential equations. Appl Math Comput 2001, 121:261-270.
22. Jang M.J., Chen C.L., Liu Y.C. On solving the initial value problems using the differential transformation method. Appl Math Comput 2000, 115:145-160.
23. Jang M.J., Chen C.L., Liu Y.C. Analysis of the response of a strongly nonlinear damped system using a differential transformation technique. Appl Math Comput 1997, 88:137-151.
24. Abdel-Halim Hassan I.H. On solving some eigenvalue problems by using a differential transformation. Appl Math Comput 2002, 127:1-22.
25. Ari{dotless}koĝlu A., Özkol I. Solution of boundary value problems for integro-differential equations by using differential transform method. Appl Math Comput 2005, 168:1145-1158.
26. Ertürk V.S., Momani S. Comparing numerical methods for solving fourth-order boundary value problems. Appl Math Comput 2007, 188(2):1963-1968.
27. Momani S., Ertürk V.S. Solutions of non-linear oscillators by the modified differential transform method. Comput Math Appl 2008, 55(4):833-842.
28. Momani S. Analytical approximate solutions of non-linear oscillators by the modified decomposition method. Int J Modern Phys C 2004, 15(7):967-979.
29. Chen C.K., Ho S.H. Solving partial differential equations by two-dimensional differential transform method. Appl Math Comput 1999, 106:171-179.
30. May R.M., Leonard W.J. Nonlinear aspects of competition between three species. SIAM J Appl Math 1975, 29:243-253.
31. Lu Z., Luo Y. Two limit cycles for a three-dimensional Lotka-Volterra. Comput Math Appl 2002, 44:51-66.
32. Olek S. An accurate solution to the multispecies Genesio equations. SIAM Rev 1994, 36(3):480-488.
33. Dehghan M., Shakourifar M., Hamidi A. The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Pade technique. Chaos Solitons Fract 2009, 39:2509-2521.
34. Dehghan M., Hamidi A., Shakourifar M. The solution of coupled Burgers equations using Adomian-Pade technique. Appl Math Comput 2007, 189:1034-1047.
35. Dehghan M., Manafian J., Saadatmandi A. Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses. Math Methods Appl Sci 2010, 33:1384-1398.
36. Dehghan M., Shakeri F. Solution of parabolic integro-differential equations arising in heat conduction in materials with memory via He's variational iteration technique. Int J Numer Methods Biomed Eng 2010, 26:705-715.
37. Dehghan M., Saadatmandi A. Variational iteration method for solving the wave equation subject to an integral conservation condition. Chaos Solitons Fract 2009, 41:1448-1453.
38. Dehghan M., Shakeri F. The numerical solution of the second Painleve equation. Numer Method Partial Differ Equa 2009, 25:1238-1259.
39. Dehghan M., Salehi R. Solution of a nonlinear time-delay model in biology via semi-analytical approaches. Comput Phys Commun 2010, 181:1255-1265.
40. Dehghan M., Salehi R. A seminumeric approach for solution of the Eikonal partial differential equation and its applications. Numer Methods Partial Differ Equa 2010, 26:702-722.
41. Dehghan M., Shakeri F. The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics. Physica Scripta 2008, 78:1-11. Article No. 06500.
42. Dehghan M., Manafian J., Saadatmandi A. Solving nonlinear fractional partial differential equations using the homotopy analysis method. Numer Meth Partial Differ Equa 2010, 26:448-479.
43. Shakeri F., Dehghan M. Solution of a model describing biological species living together using the variational iteration method. Math Comput Model 2008, 48:685-699.
44. Shakeri F., Dehghan M. Solution of delay differential equations via a homotopy perturbation method. Math Comput Model 2008, 48:486-498.