Share This Article:

Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

Abstract Full-Text HTML Download Download as PDF (Size:7765KB) PP. 175-184
DOI: 10.4236/ajcm.2013.33026    6,218 Downloads   11,418 Views   Citations

ABSTRACT

In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Mohamed and M. Torky, "Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation," American Journal of Computational Mathematics, Vol. 3 No. 3, 2013, pp. 175-184. doi: 10.4236/ajcm.2013.33026.

References

[1] S. A. Khuri, “A Laplace Decomposition Algorithm Applied to Class of Nonlinear Differential Equations,” Journal of Applied Mathematics, Vol. 1, No. 4, 2001, pp. 141-155.
[2] H. Hosseinzadeh, H. Jafari and M. Roohani, “Application of Laplace Decomposition Method for Solving Klein-Gordon Equation,” World Applied Sciences Journal, Vol. 8, No. 7, 2010, pp. 809-813.
[3] M. Khan, M. Hussain, H. Jafari and Y. Khan, “Application of Laplace Decomposition Method to Solve Nonlinear Coupled Partial Differential Equations,” World Applied Sciences Journal, Vol. 9, No. 1, 2010, pp. 13-19.
[4] E. Yusufoglu (Aghadjanov), “Numerical Solution of Duffing Equation by the Laplace Decomposition Algorithm,” Applied Mathematics and Computation, Vol. 177, No. 2, 2006, pp. 572-580. doi:10.1016/j.amc.2005.07.072
[5] T. Xu, J. Li and H.-Q. Zhang, “New Extension of the Tanh-Function Method and Application to the Whitham-Broer-Kaup Shallow Water Model with Symbolic Computation,” Physics Letters A, Vol. 369, No. 5-6, 2007, pp. 458-463. doi:10.1016/j.physleta.2007.05.047
[6] A. A. Solimana and M. A. Abdoub, “Numerical Solutions of Nonlinear Evolution Equations Using Variational Iteration Method,” Journal of Computational and Applied Mathematics, Vol. 207, No. 1, 2007, pp. 111-120. doi:10.1016/j.cam.2006.07.016
[7] E. Fan, “Soliton Solutions for a Generalized Hirota-Satsuma Coupled KdV Equation and a Coupled MKdV Equation,” Physics Letters A, Vol. 2852, No. 1-2, 2001, pp. 18-22. doi:10.1016/S0375-9601(01)00161-X
[8] H. Jafari and V. Daftardar-Gejji, “Solving Linear and Nonlinear Fractional Diffution and Wave Equations by Adomian Decomposition,” Applied Mathematics and Computation, Vol. 180, No. 2, 2006, pp. 488-497. doi:10.1016/j.amc.2005.12.031
[9] F. Abdelwahid, “A Mathematical Model of Adomian Polynomials,” Applied Mathematics and Computation, Vol. 141, No. 2-3, 2003, pp. 447-453. doi:10.1016/S0096-3003(02)00266-7
[10] T. A. Abassya, M. A. El-Tawil and H. El-Zoheiry, “Exact Solutions of Some Nonlinear Partial Differential Equations Using the Variational Iteration Method Linked with Laplace Transforms and the Pade Technique,” Computers and Mathematics with Applications, Vol. 54, No. 7-8, 2007, pp. 940-954. doi:10.1016/j.camwa.2006.12.067

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.