Comparing numerical methods for boussinesq equation model problem

Numerical Methods for Partial Differential Equations

Volumn 25, Issue 4, 2009, Pages 783-796

  Bulut, Hasan ^a  

^a FIRAT UNIVERSITY   (Turkey)

Author keywords

Adomian decomposition method; Boussinesq equation; Homotopy perturbation method; Nonlinear partial differential equations; Variational iteration method

Indexed keywords

EID: 67849090333     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20372     Document Type: Article

References (25)

1. 1 J. H. He, Some asymptotic methods for strongly nonlinear equations, Int J Mod Phys B 20 (2006), 1141–1148.
2. 2 J. H. He, Variational iteration method a kind of non‐linear analytical technique: some examples, Int J Non‐Linear Mech 34 (1999), 699–708.
3. 3 A. M. Wazwaz, Adomian decomposition method for a reliable treatment of the Bratu‐type equations, Appl Math Comput 166 (2005), 652–663.
4. 4 A. M. Wazwaz and A. Gorgius, Exact solutions for heat‐like and wave‐like equations with variable coefficients, Appl Math Comput 149 (2004), 15–29.
5. 5 A. M. Wazwaz, A new algorithm for calculating adomian polynomials for nonlinear operators, Appl Math Comput 111 (2000), 33–51.
6. 6 D. Lesnic, Blow‐up solutions obtained using the decomposition method, Chaos Solitons Fractals 28 (2006), 776–787.
7. 7 S. Saha Ray, A numerical solution of the coupled sine‐Gordon equation using the modified decomposition method, Appl Math Comput 175 (2006), 1046–1054.
8. 8 J. H. He and X.‐H. Wu, Exp‐ function method for nonlinear wave equations, Chaos Solitons Fractals 30 (2006), 700–708.
9. 9 J. H. He, Variational iteration method for autonomous ordinary differential systems, Appl Math Comput 11 (2000), 115–124.
10. 10 D. D. Ganji and A. Sadighi, Application of homotopy ‐ perturbation and variational iteration methods to nonlinear heat transver and porous media equations, J Comput Appl Math 207 (2007), 24–34.
11. 11 J. H. He, A coupling method a homotopy technique and a perturbation technique for non‐linear problems, Int J Non‐Linear Mech 35 (2000), 37–43.
12. 12 D. Kaya and H. Bulut, On a Numerical Comparison of Decomposition Method and Finite Difference Method for an Elliptic P.D.E Firat Üniv Fen ve Müh Bilimleri Dergisi 11 (1999), 285–291.
13. 13 G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publisher, Boston, 1994.
14. 14 J. H. He, Homotopy Pertubation Method for Bifurcation of Nonlinear Problems, Int J Nonlinear Sci Simul 6 (2005), 207–209.
15. 15 G. Adomian, A new approach to nonlinear partial differential equations, J Mathematical Analysis and Applications 102 (1984), 420–434.
16. 16 D. D Ganji, The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer, Phys Lett A 355 (2006), 337–341.
17. 17 A. D. Polyanin, Handbook of Linear Partial Differential Equaitons for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton, 2002.
18. 18 J. H. He, Application of He's Homotopy‐perturbation Method to Nonlinear Coupled System of Reaction‐ diffusion Equations, Int J Nonlinear Sci Simul 7 (2006), 413–420.
19. 19 J. H. He and M. A. Abdou, New periodic solutions for nonlinear evolution equations using Exp‐function method, Chaos Solitons Fractals 34 (2007), 1421–1429.
20. 20 J. H. He, Non‐perturbative methods for strongly nonlinear problems, PhD dissertation, Verlag im Internet GmbH, Berlin, 2006.
21. 21 A. Rajabi, D. D Ganji, and H. Taherian, Application of homotopy perturbation method in nonlinear heat conduction and convection equations, Phys Lett A 360 (2007), 570–573.
22. 22 A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder, Phys Lett A 352 (2006), 404–410.
23. 23 A. Sommerfeld, Partial Differential Equations in Physics, Academic Press, New York, 1999.
24. 24 N. Bellomo and D. Sarafyan, On Adomian's decomposition method and some comparisons with Picard's iterative scheme, J Math Anal Appl 123 (1987), 389–400.
25. 25 D. S. Momani and S. Abuasad, Application of He's variational iteration method to Helmholtz equation, Chaos Solitons Fractals 27 (2006), 1119–1123.