The solution of Burgers' and good Boussinesq equations using ADM-Padé technique

Chaos, Solitons and Fractals

Volumn 32, Issue 3, 2007, Pages 1008-1026

  Abassy, Tamer A ^a   El Tawil, Magdy A ^b   Saleh, Hassan K ^b  

^a BENHA UNIVERSITY   (Egypt)

^b CAIRO UNIVERSITY   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

ADOMIAN DECOMPOSITION METHOD (ADM); APPROXIMANTS; BURGERS' AND BOUSSINESQ EQUATION; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 33845229154     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.11.029     Document Type: Article

References (35)

1. Abassy T.A., El-Tawil M., and Kamel H. The solution of KdV and mKdV equations using Adomian Padé approximation. Int J Nonlinear Sci Numer Simulat 5 4 (2004) 327-339
2. Abboui K., and Cherruault Y. Convergence of Adomian method applied to differential equations. Comput Math Appl 28 5 (1994) 103-109
3. Ablowitz M.J., and Segur H. Solitons and the inverse scattering transform (1981), SIAM, Philadelphia (PA)
4. Adomian G. Solving frontier problem of physics: the decomposition method (1994), Kluwer Academic Publishers, Boston (MA)
5. Andreev V.K., Kabstov O.V., Pukhnachov V.V., and Rodionov A.A. Applications of group-theoretical methods in hydrodynamics (1998), Kluwer Academic Publishers, Boston
6. Baker Jr. G.A. Essentials of Padè approximants (1975), Academic Press, London
7. Bateman H. Some recent researches on the motion of fluids. Mon Weather Rev 43 (1915)
8. Bratsos A.G. The solution of the Boussinesq equation using the method of lines. Comput Meth Appl Mech Eng 157 (1998) 33-44
9. Burgers J.M. Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion. Trans Roy Neth Acad Sci, Amsterdam 17 (1939) 1-53
10. Cole J.D. On a quasi-linear parabolic equation occurring in aerodynamics. Quart Appl Math 9 (1951) 225-236
11. Debnath L. Nonlinear partial differential equations for scientists and engineers (1998), Brikhauser, Berlin
12. Debnath L. Nonlinear water waves (1994), Academic Press, Boston
13. Drazin P.G., and Jonson R.S. Soliton: an introduction (1993), Cambridge University Press, New York
14. Fletcher C.A.J. Burgers' equation: a model for all reasons. In: Noye J. (Ed). Numerical solutions of partial differential equations (1982), North-Holland Pub. Co., Amsterdam
15. He J.H. A review on some new recently developed nonlinear analytical techniques. Int J Nonlinear Sci Numer Simulat 1 1 (2000) 51-70
16. He J.H. Variational iteration method: a kind of nonlinear analytical technique: some examples. Int J Nonlinear Mech 34 4 (1999) 699-708
17. He J.H. Variational iteration method for autonomous ordinary differential system. Appl Math Comput 114 2/3 (2000) 115-123
18. He J.H., Wan Y.Q., and Guo Q. An iteration formulation for normalized diode characteristics. Int J Circ Theory Appl 32 6 (2004) 629-632
19. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput Meth Appl Mech Eng 167 1-2 (1998) 57-68
20. He J.H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput Meth Appl Mech Eng 167 1-2 (1998) 69-73
21. Hirota R. Direct methods in soliton theory. In: Bullogh R.K., and Caudrey P.J. (Eds). Solitons (1980), Springer, Berlin
22. Hirota R. Exact envelope-soliton solutions of a nonlinear wave. J Math Phys 14 7 (1973) 805-809
23. Hirota R. Exact N-soliton solutions of the wave equation of long waves in shallow water and in nonlinear lattices. J Math Phys 14 7 (1973) 810-814
24. xx. Commun Pure Appl Math 3 (1950) 201-230
25. Jiao Y.C., Yamamoto Y., Dang C., and Hao Y. An after treatment technique for improving the accuracy of Adomian's decomposition method. Comput Math Appl 43 (2002) 783-798
26. Kabstov O.V. Construction of exact solutions of the Boussinesq equation. J Appl Mech Tech Phys 39 3 (1998) 389-392
27. Lyle CS. Finite element approximations of Burgers' equation with Robin's boundary conditions. MSc thesis, The Faculty of the Virginia Polytechnic Institute and State University, 1997.
28. Mckean H.P. Boussinesq equation on the circle. Commun Pure Appl Math 34 (1981) 599-691
29. Manoranjan V.S., Mitchell A.R., and Morris J.L. Numerical solutions of the "good" Boussinesq equation. SIAM J Sci Stat Comput 5 (1984) 946-957
30. Manoranjan V.S., Ortega T., and Sang-Seran J.M. Soliton and antisoliton interactions in the "good" Boussinesq equation. J Math Phys 29 (1988) 1964-1968
31. Nimmo J.J.C., and Freeman N.C. A method of obtaining the n-soliton solutions of the Boussinesq equation in terms of Wronskian. Phys Lett A 95 (1983) 4-6
32. Nimmo J.J.C., and Freeman N.C. The use of Bäcklund transformations in obtaining the N-soliton solutions in Wronskian form. J Phys A 17 (1984) 1415-1424
33. Ortega T., and Sang-Seran J.M. Nonlinear stability and convergence of finite-difference methods for the "good" Boussinesq equation. Numer Math 58 (1990) 215-229
34. Wazwaz A.M. Analytical approximations and Padé approximants for Volterra's population model. Appl Math Comput 100 (1999) 13-25
35. Wazwaz A.M. Construction of soliton solutions and periodic solutions of the Boussinesq equation by modified decomposition method. Chaos, Solitons & Fractals 12 (2001) 1549-1556