Numerical solutions for the damped generalized regularized long-wave equation with a variable coefficient by Adomian decomposition method

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 5, 2009, Pages 2025-2033

  Achouri, Talha ^a   Omrani, Khaled ^b  

^a FACULTÉ DES SCIENCES DE MONASTIR   (Tunisia)

^b INSTITUT SUPÉRIEUR DES SCIENCES APPLIQUÉES ET DE TECHNOLOGIE DE SOUSSE   (Tunisia)

Author keywords

02.60.Lj; 44.05.+e; 44.10.+I; Adomian decomposition method; DGRLW equation; Error analysis; Modified decomposition method; Numerical solution

Indexed keywords

ERROR ANALYSIS; NUMERICAL METHODS; WAVE EQUATIONS;

+E; +I; 02.60.; 44.05.; 44.10.; ADOMIAN DECOMPOSITION METHOD; DAMPED GENERALIZED REGULARIZED LONG-WAVE EQUATION; GENERALIZED REGULARIZED LONG-WAVE EQUATIONS; LJ; MODIFIED DECOMPOSITION METHOD; NUMERICAL SOLUTION;

NONLINEAR EQUATIONS;

EID: 56249140400     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2008.07.011     Document Type: Article

References (23)

1. Benjamin T.B., Bona J.L., and Mahony J.J. Model equations for long waves in nonlinear dispersive systems. Philos Trans Roy Soc London, A 272 (1972) 47-78
2. Peregrine D.H. Calculations of the development of an undular bore. J Fluid Mech 25 (1966) 321-326
3. Mei M. Large-time behavior of solution for generalized Benjamin-Bona-Mahony-Burgers equations. Nonlinear Anal 33 (1998) 699-714
4. Dura A., and Lopez-Marcos M.A. Numerical behavior of stable and unstable solitary waves. Appl Numer Math 42 (2002) 95-116
5. Zhang H., Wei G.M., and Gao Y.T. On the general form of the Benjamin-Bona-Mahony equation in fluid mechanics. Czech J Phys 52 (2002) 344-373
6. Kadri T, Khiari N, Abidi F, Omrani K. Methods for the numerical solution of the Benjamin-Bona-Mahony-Burgers equation. Numer Meth Partial Diff Eq, in press.
7. Achouri T, Ayadi M, Omrani K. A fully Galerkin method for the damped generalized regularized long-wave (DGRLW) equation. Numer Meth Partial Diff Eq, in press.
8. Achouri T., Khiari N., and Omrani K. On the convergence of difference schemes for the Benjamin-Bona-Mahony (BBM) equation. Applied Math Comput 182 (2006) 999-1005
9. Omrani K., and Ayadi M. Finite difference discretization of the Benjamin-Bona-Mahony-Burgers (BBMB) equation. Numer Meth Partial Diff Eq 24 1 (2008) 239-248
10. Wahlbin L. Error estimates for a Galerkin method for a class of model equations for long waves. Numer Math 23 (1975) 289-303
11. Ewing R.E. Time-stepping Galerkin methods for nonlinear Sobolev partial differential equation. IAM J Numer Anal 15 (1978) 1125-1150
12. Arnold D.N., Douglas Jr. J., and Thomée V. Superconvergence of finite element approximation to the solution of a Sobolev equation in a single space variable. Math Comput 27 (1981) 737-743
13. Omrani K. The convergence of the fully discrete Galerkin approximations for the Benjamin-Bona-Mahony (BBM) equation. Applied Math Comput 180 2 (2006) 614-621
14. Adomian G. Solving frontier problems of physics: the decomposition method (1999), Kluwer Academic Publishers, Boston
15. Adomian G. A review of the decomposition method in applied mathematics. J Math Anal Appl 135 (1988) 501-544
16. Kaya D., and El-Sayed S.M. An application of the decomposition method for the generalized KdV and RLW equations. Chaos Solitons Fractals 17 (2003) 869-877
17. Al-Khaled K., Momani S., and Alawneh A. Approximate wave solutions for generalized Benjamin-Bona-Mahony-Burgers equations. Appl Math Comp 171 (2005) 281-292
18. Kaya D. A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation. Appl Math Comput 149 (2004) 833-841
19. El-Danaf T.S., Ramadan M.A., and Abd Alaal F.F.I. The use Adomian decomposition method for solving the regularized long-wave equation. Chaos Solitons Fractals 26 (2005) 747-757
20. Wazwaz A.M. A reliable modification of Adomian decomposition method. Appl Math Comput 102 (1999) 77-86
21. Wazwaz A.M. A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl Math Comput 111 (2000) 53-69
22. Wazwaz A.M. The existence of noise terms for systems of inhomogeneous differential and integral equations. Appl Math Comput 146 1 (2003) 81-92
23. Saha Ray S., Chaudhuri K.S., and Bera R.K. Application of modified decomposition method for the analytical solution of space fractional diffusion equation. Appl Math Comput 196 (2008) 294-302