On numerical solution of Burgers' equation by homotopy analysis method

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 372, Issue 4, 2008, Pages 356-360

  Inc, Mustafa ^a  

^a FIRAT UNIVERSITY   (Turkey)

Author keywords

Burgers' equation; Homotopy analysis method; Series solution

Indexed keywords

NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES;

AUXILIARY PARAMETERS; BOUNDARY AND INITIAL CONDITIONS; BURGERS' EQUATIONS; HOMOTOPY ANALYSIS METHODS; HOMOTOPY PERTURBATION METHOD (HPM); INITIAL APPROXIMATION; ONE DIMENSIONAL NON-LINEAR BURGERS' EQUATION; SERIES SOLUTIONS;

NUMERICAL METHODS;

EID: 37549023840     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2007.07.057     Document Type: Article

References (38)

1. Aksan E.N. Appl. Math. Comput. 174 (2006) 884
2. Kutluay S., and Esen A. Int. J. Comput. Math. 81 (2004) 1433
3. Abbasbandy S., and Darvishi M.T. Appl. Math. Comput. 163 (2005) 1265
4. Sirendaoreji. J. Phys. A: Math. Gen. 32 (1999) 6897
5. Tian B., and Gao Y. J. Phys. A: Math. Gen. 29 (1996) 2895
6. Bateman H. Mon. Weather Rev. 43 (1915) 163
7. Burgers J.M. Proc. R. Nether. Acad. Sci. Amsterdam 43 (1940) 2
8. Hopf E. Commun. Pure Appl. Math. 3 (1950) 201
9. Cole J.D. Quart. Appl. Math. 9 (1951) 225
10. Benton E.R., and Platzman G.W. Quart. Appl. Math. 30 (1972) 195
11. Karpman V.I. Nonlinear Waves in Dispersive Media (1975), Pergamon, Oxford
12. Özdeş A., Kutluay S., Bahadir A.R., and Şahin A. Balkan Phys. Lett. 4 (1996) 251
13. Varoǧlu E., and Finn D.L. Int. J. Numer. Methods Eng. 16 (1980) 171
14. Caldwell J., and Smith P. Appl. Math. Model. 6 (1982) 381
15. Evans D.J., and Abdullah A.R. Computing 32 (1984) 239
16. Kakuda K., and Tosaka N. Int. J. Numer. Methods Eng. 29 (1990) 245
17. Mittal R.C., and Singhal P. Commun. Numer. Methods Eng. 9 (1993) 397
18. Ali A.H.A., Gardner G.A., and Gardner L.R.T. Comput. Methods Appl. Mech. Eng. 100 (1992) 325
19. Nguyen N., and Reynen J. Numer. Methods Nonlinear Prob. 2 (1982) 718
20. Miller K., and Miller R. SIAM J. Numer. Anal. 18 (1981) 1019
21. Herbest B.M., Schoombie S.W., and Mitchell A.R. Int. J. Numer. Methods Eng. 36 (1993) 3317
22. Gardner L.R.T., Gardner G.A., and Dogan A. Arabian J. Sci. Eng. 22 (1997) 100
23. Öziş T., Aksan E.N., and Özdeş A. Appl. Math. Comput. 139 (2003) 417
24. Abbasbandy S., and Darvishi M.T. Appl. Math. Comput. 170 (2005) 95
25. S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, PhD thesis, Shanghai Jiao Tong University, 1992
26. Liao S.J. Int. J. Non-Linear Mech. 34 (1999) 759
27. Liao S.J. Beyond Perturbation: Introduction to the Homotopy Analysis Method (2003), Champan and Hall/CRC Press, Boca Raton
28. Liao S.J. J. Fluid Mech. 488 (2003) 189
29. Liao S.J. Appl. Math. Comput. 147 (2004) 499
30. Liao S.J. Int. J. Heat Mass Transfer 48 (2005) 2529
31. Ayub M., Rasheed A., and Hayat T. Int. J. Eng. Sci. 41 (2003) 2091
32. Hayat T., and Khan M. Nonlinear Dynam. 42 (2005) 395
33. Hayat T., Khan M., and Ayub M. Z. Angew. Math. Phys. 56 (2005) 1012
34. Wu W., and Liao S.J. Chaos Solitons Fractals 26 (2005) 177
35. Abbasbandy S. Phys. Lett. A 360 (2006) 109
36. Hayat T., and Sajid M. Phys. Lett. A 361 (2007) 316
37. Abbasbandy S. Phys. Lett. A 361 (2007) 478
38. He J.H. Int. J. Mod. Phys. B 20 (2006) 1141