International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 4, Issue 8  (August 2017), Pages:  98-103

Title: Successive approximation method for solving (1+1)-dimensional dispersive long wave equations

Author(s):  Saad A. Manaa *, Fadhil H. Easif, Bewar Y. Ali

Affiliation(s):

Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region, Iraq

https://doi.org/10.21833/ijaas.2017.08.014

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Abstract:

In this paper, we study the (1+1)-dimensional dispersive long wave equations which describe the evolution of horizontal velocity component u(x,t) of water waves of height v(x,t), and solved it numerically by successive approximation method (SAM) to compare with Adomian’s decomposition method (ADM), we found that SAM is suitable for this kind of problems also its effective and more accure than ADM. Mathematica has been used for computations. 

© 2017 The Authors. Published by IASE.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Successive approximation method, Adomain decomposition method, (1+1)-dimensional dispersive long wave equations

Article History: Received 30 March 2017, Received in revised form 8 July 2017, Accepted 17 July 2017

Digital Object Identifier: 

https://doi.org/10.21833/ijaas.2017.08.014

Citation:

Manaa SA, Easif FH, and Ali BY (2017). Successive approximation method for solving (1+1)-dimensional dispersive long wave equations. International Journal of Advanced and Applied Sciences, 4(8): 98-103

http://www.science-gate.com/IJAAS/V4I8/Manaa.html

References:

  1. Ablowitz MJ and Clarkson PA (1991). Solitons, nonlinear evolution equations and inverse scattering. Cambridge University Press, Cambridge, UK. https://doi.org/10.1017/CBO9780511623998
  2. Bai CL, Zhao H, and Han JG (2006). Application of an extended homogeneous balance method to new exact solutions of nonlinear evolution equations. Czechoslovak Journal of Physics, 56(3): 237-242. https://doi.org/10.1007/s10582-006-0084-8
  3. Boiti M, Leon JJP, and Pempinelli F (1987). Spectral transform for a two spatial dimension extension of the dispersive long wave equation. Inverse Problems, 3(3): 371-387. https://doi.org/10.1088/0266-5611/3/3/007
  4. Broer LJF (1975). Approximate equations for long water waves. Applied Scientific Research, 31(5): 377-395. https://doi.org/10.1007/BF00418048
  5. Coddington EA (1995). An introduction to ordinary differential equations. Prentice Hall of India, New Delhi, India.
  6. Eckhaus W (1985). Preprint 404. University of Utrecht, Utrecht, Netherlands.        PMid:4077652
  7. Jerri A (1999). Introduction to integral equations with applications. John Wiley and Sons, Hoboken, USA.
  8. Kaup DJ (1975). A higher-order water-wave equation and the method for solving it. Progress of Theoretical Physics, 54(2): 396-408. https://doi.org/10.1143/PTP.54.396
  9. Kupershmidt BA (1985). Mathematics of dispersive water waves. Communications in Mathematical Physics, 99(1): 51-73. https://doi.org/10.1007/BF01466593
  10. Mohamed MA (2010). Comparison differential transformation technique with adomian decomposition method for dispersive long-wave equations in (2+1)-dimensions. Applications and Applied Mathematics: An International Journal (AAM), 5(1): 148-166.
  11. Saeed RK (2006). Computational methods for solving system of linear volterra integral and integro-differential equations. Ph.D. Dissertation, University of Salahaddin/Erbil-Collage of Science, Erbil, Iraqi Kurdistan.
  12. Wang M, Zhou Y, and Li Z (1996). Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Physics Letters A, 216(1–5): 67-75. https://doi.org/10.1016/0375-9601(96)00283-6