Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method

Applied Mathematics and Computation

Volumn 217, Issue 16, 2011, Pages 7001-7008

  Liu, Jincun ^a   Hou, Guolin ^a  

^a INNER MONGOLIA UNIVERSITY   (China)

Author keywords

Caputo fractional derivative; Differential transform method; Fractional coupled Burgers equations; Generalized Taylor series formula; Numerical solutions

Indexed keywords

CAPUTO FRACTIONAL DERIVATIVES; DIFFERENTIAL TRANSFORM METHOD; FRACTIONAL COUPLED BURGERS EQUATIONS; GENERALIZED TAYLOR SERIES FORMULA; NUMERICAL SOLUTION;

DIFFERENTIATION (CALCULUS); FLOW MEASUREMENT; POLYNOMIALS; TAYLOR SERIES; TWO DIMENSIONAL;

NUMERICAL METHODS;

EID: 79952454335     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.01.111     Document Type: Article

References (25)

1. C.P. Li, and Y.H. Wang Numerical algorithm based on Adomian decomposition for fractional differential equations Comput. Math. Appl. 57 10 2009 1672 1681
2. S.R. Santanu Analytical solution for the space fractional diffusion equation by two-step Adomian decomposition method Commun. Nonlinear. Sci. Numer. Simulat. 14 4 2009 1295 1306
3. M.R. Yulita, M.S.M. Nooran, and I. Hashim Variational iteration method for fractional heat- and wave-like equations Nonlinear Anal. Real World Appl. 10 3 2009 1854 1869
4. I. Mustafa The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method J. Math. Anal. Appl. 345 1 2008 476 484
5. H. Jafari, and S. Seifi Solving a system of nonlinear fractional partial differential equations using homotopy analysis method Commun. Nonlinear. Sci. Numer. Simulat. 14 5 2009 1962 1969
6. H. Xu, S.J. Liao, and X.C. You Analysis of nonlinear fractional partial differential equations with the homotopy analysis method Commun. Nonlinear. Sci. Numer. Simulat. 14 4 2009 1152 1156
7. Y. Zhang A finite difference method for fractional partial differential equation Appl. Math. Comput. 215 2 2009 524 529
8. S. Chen, F. Liu, P. Zhuang, and V. Anh Finite difference approximations for the fractional Fokker-Planck equation Appl. Math. Model. 33 1 2009 256 273
9. Y. Chen, and H.L. An Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives Appl. Math. Comput. 200 1 2008 87 95
10. J.K. Zhou Differential Transformation and its Applications for Electric Circuits 1986 Huazhong Univ. Press Wuhan, China in Chinese
11. C.K. Chen, and S.H. Ho Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform Int. J. Mech. Sci. 41 11 1999 1339 1356
12. M.J. Jang, C.L. Chen, and Y.C. Liy On solving the initial value problems using differential transformation method Appl. Math. Comput. 115 2-3 2000 145 160
13. A.S. V Ravi Kanth, and K. Aruna Solution of singular two-point boundary value problems using differential transformation method Phys. Lett. A 372 26 2008 4671 4673
14. A. Fatma Solutions of the system of differential equations by differential transform method Appl. Math. Comput. 147 12 2004 547 567
15. S.H. Chang, and I.L. Chang A new algorithm for calculating one-dimensional differential transform of nonlinear functions Appl. Math. Comput. 195 2 2008 799 808
16. C.K. Chen, and S.H. Ho Solving partial differential equations by two-dimensional differential transform method Appl. Math. Comput. 106 2-3 1999 171 179
17. S.H. Chang, and I.L. Chang A new algorithm for calculating two-dimensional differential transform of nonlinear functions Appl. Math. Comput. 215 7 2009 2486 2494
18. A.S. V Ravi Kanth, and K. Aruna Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations Chaos Solitons Fract. 41 5 2009 2277 2281
19. A.S. V Ravi Kanth, and K. Aruna Differential transform method for solving the linear and nonlinear Klein-Gordon equation Comput. Phys. Commun. 180 5 2009 708 711
20. Z. Odibata, and S. Momani A generalized differential transform method for linear partial differential equations of fractional order Appl. Math. Lett. 21 2 2008 194 199 (Pubitemid 350181314)
21. S. Momani, Z. Odibat, and V.S. Erturk Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation Phys. Lett. A 370 5-6 2007 379 387
22. M. Kurulay, and M. Bayram Approximate analytical solution for the fractional modified KdV by differential transform method Commun. Nonlinear. Sci. Numer. Simulat. 15 7 2010 1777 1782
23. I. Podlubny Fractional Differential Equations 1999 Academic Press New York
24. M. Caputo Linear models of dissipation whose Q is almost frequency independent, Part II J. Roy. Austral. Soc. 13 1967 529 539
25. S. Momani, and Z. Odibat A novel method for nonlinear fractional partial differential equations: combination of DTM and generalized Taylors formula J. Comput. Appl. Math. 220 1-2 2008 85 95