Comparison of the solutions obtained by B-spline FEM and ADM of KdV equation

Applied Mathematics and Computation

Volumn 169, Issue 1, 2005, Pages 146-156

  Geyikli, Turabi ^a   Kaya, Doǧan ^a,b  

^a INONU UNIVERSITY   (Turkey)

^b FIRAT UNIVERSITY   (Turkey)

Author keywords

Galerkin method; Korteweg de Vries equation; Soliton solution; Splines finite element method; The decomposition method

Indexed keywords

GALERKIN METHODS; NONLINEAR EQUATIONS; PROBLEM SOLVING; RELIABILITY; SOLITONS;

KORTEWEG-DE VRIES (KDV) EQUATION; SOLITON SOLUTION; SPLINES FINITE ELEMENT METHOD; THE DECOMPOSITION METHOD;

FINITE ELEMENT METHOD;

EID: 27144546034     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.10.045     Document Type: Article

References (42)

1. P.G. Drazin, and R.S. Johnson Solutions: an Introduction 1989 Cambridge University Press Cambridge
2. G.B. Whitham Linear and Nonlinear Waves 1974 John Wiley and Sons New York
3. R.B. Guenther, and J.W. Lee Partial Differential Equations of Mathematical Physics and Integral Equations 1988 Dover Publications New York
4. G. Adomian Appl. Math. Comput. 88 1971 131
5. D. Kaya Int. J. Comp. Math. 72 1999 531
6. G. Adomian Solving Frontier Problems of Physics: the Decomposition Method 1994 Kluwer Academic Publishers Boston
7. N.J. Zabusky W. Ames Proc. Symp. Non-linear Partial Diff. Equations 1967 Academic Press New York 223
8. B. Fornberg, and G.B. Whitham Phil. Trans. Roy. Soc. 289 1978 373
9. J.M. Sanz Serna, and I. Christie J. Comp. Phys. 39 1981 94
10. G.A. Gardner, A.H.A. Ali, and L.R.T. Gardner R. Gruber J. Periaux R.P. Shaw ISNME-89 vol. 2 1989 Springer-Verlag New York 565
11. G.A. Gardner, L.R.T. Gardner, and A.H.A. Ali G. Cohen Mathematical & Numerical Aspects Wave Propagation, 1991 1991 SIAM Philadelphia 533
12. G.A. Gardner, L.R.T. Gardner, and A.H.A. Ali Comp. Meth. Appl. Mech. Engng. 92 1991 231
13. G. Adomian J. Math. Anal. Appl. 135 1988 501
14. G. Adomian Nonlinear Stochastic Operator Equations 1986 Academic Press San Diego, CA
15. D.J. Korteweg, and G. de Vries Philos. Mag. 39 1895 422
16. M.C. Shen SIAM J. Appl. Math. 17 1969 260
17. C.S. Gardner J. Math. Phys. 12 1971 1548
18. C.S. Gardner, J.M. Greene, M.D. Kruskal, and R.M. Miura Comm. Pure Appl. Math. XXVII 1974 97
19. D. Kaya, and S.M. El-Sayed Phys. Lett. A 310 2003 44
20. D. Kaya, and M. Aassila Phys. Lett. A 299 2002 201
21. V. Seng, K. Abbaoui, and Y. Cherruault Math. Comput. Model. 24 1996 59
22. A.M. Wazwaz Appl. Math. Comput. 102 1999 77
23. P. Saucez, A.V. Wouwer, and W.E. Schiesser Comput. Math. Appl. 35 1998 13
24. G. Adomian, and R. Rach Comput. Math. Appl. 24 1992 61
25. A.M. Wazwaz J. Math. Anal. Appl. 5 1997 265
26. Y. Cherruault Kybernetes 18 1989 31
27. A. Repaci Appl. Math. Lett. 3 1990 35
28. Y. Cherruault, and G. Adomian Math. Comput. Model. 18 1993 103
29. K. Abbaoui, and Y. Cherruault Comput. Math. Appl. 28 1994 103
30. K. Abbaoui, and Y. Cherruault Comput. Math. Appl. 29 1995 103
31. K. Abbaoui, M.J. Pujol, Y. Cherruault, N. Himoun, and P. Grimalt Kybernetes 30 2001 1183
32. L.R.T. Gardner, G.A. Gardner, T. Geyikli, U.C.N.W. Maths Preprint, 91.28, 1991.
33. L.R.T. Gardner, G.A. Gardner, and T. Geyikli Advances in Modelling & Analysis, A vol. 18 1994 AM SE Press New York p. 31
34. L.R.T. Gardner, G.A. Gardner, and T. Geyikli Comp. Meth. Appl. Mech. Engng. 124 1995 321
35. D. Kaya, and S.M. El-Sayed Phys. Lett. A 313 2003 82
36. D. Kaya Appl. Math. Comp. 147 2004 69
37. D. Kaya, and I.E. Inan Appl. Math. Comp. 151 2004 775
38. D. Kaya, and A. Yokus Math. Comp. Simul. 60 2002 507
39. D. Kaya, and S.M. El-Sayed Chaos, Solitons & Fractals 17 2003 869
40. D. Kaya Appl. Math. Comp. 143 2003 309
41. D. Kaya Appl. Math. Comp. 152 2004 253
42. D. Kaya Appl. Math. Comp. 152 2004 709