An application of the ADM to seven-order Sawada-Kotara equations

Applied Mathematics and Computation

Volumn 157, Issue 1, 2004, Pages 93-101

  El Sayed, Salah M ^a,c   Kaya, Doǧan ^b  

^a BENHA UNIVERSITY   (Egypt)

^b FIRAT UNIVERSITY   (Turkey)

^c Girls College of Education Riyadh   (Saudi Arabia)

Author keywords

Lax's seventh order KdV equation; Solitary wave solution; The Adomian decomposition method; The convergence of Adomian decomposition method; The seventh order Sawada Kotera equation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INTEGRATION; LINEARIZATION; MATHEMATICAL OPERATORS; PROBLEM SOLVING;

SOLITARY WAVE SOLUTIONS; THE ADOMIAN DECOMPOSITION METHOD; THE CONVERGENCE OF ADOMIAN DECOMPOSITION METHOD; THE SEVENTH ORDER SAWADA KOTERA EQUATION;

WAVE EQUATIONS;

EID: 4344646714     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.08.104     Document Type: Article

References (16)

1. Hereman W., Banerjee P.P., Korpel A., Assanto G., van Immerzeele A., Meerpoel A. Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method. J. Phys. A: Math. Gen. 19:1986;607-628.
2. Parkes E.J., Duffy B.R. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput. Phys. Commun. 98:1996;288-300.
3. Kaya D. On the solution of a Korteweg-de Vries like equation by the decomposition method. Int. J. Comput. Math. 72:1999;531-539.
4. Kaya D., Inan I.E. On the Sawada-Kotare equation. J. Inst. Math. Comput. Sci. 14:2001;117-119.
5. Kaya D., Aassila M. An application for a generalized KdV equation by decomposition method. Phys. Lett. A. 299:2002;201-206.
6. Kaya D. An explicit and numerical solutions of some fifth-order KdV equation by decomposition method. Appl. Math. Comput. 144:2003;353-363.
7. Kaya D., El-Sayed Salah M. An application of the decomposition method for the generalized KdV and RLW equations. Chaos Solitons Fract. 17:2003;869-877.
8. Kaya D., El-Sayed Salah M. On a generalized fifth order KdV equations. Phys. Lett. A. 310:2003;44-51.
9. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method. 1994;Kluwer Academic Publishers, Boston, MA.
10. Adomian G. A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135:1988;501-544.
11. Wazwaz A.M. A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. Math. Comput. 111:2000;53-69.
12. Seng V., Abbaoui K., Cherruault Y. Adomian's polynomials for nonlinear operators. Math. Comput. Modell. 24:1996;59-65.
13. Abbaoui K., Cherruault Y. Convergence of Adomian's method applied to differential equations. Comput. Math. Appl. 28:1994;103-109.
14. Abbaoui K., Cherruault Y. New ideas for proving convergence of decomposition methods. Comput. Math. Appl. 29:1995;103-108.
15. Abbaoui K., Pujol M.J., Cherruault Y., Himoun N., Grimalt P. A new formulation of Adomian method: convergence result. Kybernetes. 30:2001;1183-1191.
16. Ngarhasta N., Some B., Abbaoui K., Cherruault Y. New numerical study of Adomian method applied to a diffusion model. Kybernetes. 31:2002;61-75.