Research Article

Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations

Volume: 1 Number: 4 December 20, 2018
EN

Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations

Abstract

In this paper, a combined form of homotopy analysis method with Aboodh transform method is proposed to solve nonlinear system of partial differential equations. This method is called the homotopy analysis Aboodh transform method (HAATM). The homotopy analysis Aboodh transform method can easily be applied to many problems of nonlinear system, and is capable of reducing the size of computational work.

Keywords

Aboodh transform method,Homotopy analysis method,Nonlinear system of partial differential equationS

References

  1. [1] N. Taghizadeh, M. Akbaria, M. Shahidia, Homotopy perturbation method and reduced differential transform method for solving (1+1)-dimensional nonlinear boussinesq equation, Int. J. Appl. Math. Comput., 5(2) (2013), 28-33.
  2. [2] S. J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, 1992.
  3. [3] S. J. Liao, Beyond perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall/CRC Press, Boca Raton, 2003.
  4. [4] S. J. Liao, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput., 147 (2004), 499-513.
  5. [5] S. J. Liao, Notes on the homotopy analysis method: Some definitions and theorems, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 983-997.
  6. [6] M. Ayub, A. Rasheed and T. Hayat, Exact flow of a third grade fluid past a porous plate using homotopy analysis method, Int. J. Eng. Sci., 41 (2003), 2091-2103.
  7. [7] S. Abbasbandy, The application of homotopy analysis method to nonlinear equations arising in heat transfer, Phys. Lett. A, 360 (2006), 109-113.
  8. [8] Z. Abbasa, S. Vahdatia, F. Ismaila, A. K. Dizicheha, Application of homotopy analysis method for linear integro-differential equations, Int. Math. Forum., 5(5) (2010) 237-249.
  9. [9] V. G. Gupta, S. Gupta, Applications of homotopy analysis transform method for solving various nonlinear equations, W. Appl. Sci. J., 18(12), (2012), 1839-1846.
  10. [10] M. M. Khader, S. Kumar, S. Abbasbandy, New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology, Chin. Phys B., 22(11), (2013), 1-5.
APA
Hamdi Cherif, M., & Ziane, D. (2018). Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations. Universal Journal of Mathematics and Applications, 1(4), 244-253. https://doi.org/10.32323/ujma.407774
AMA
1.Hamdi Cherif M, Ziane D. Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations. Univ. J. Math. Appl. 2018;1(4):244-253. doi:10.32323/ujma.407774
Chicago
Hamdi Cherif, Mountassir, and Djelloul Ziane. 2018. “Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations”. Universal Journal of Mathematics and Applications 1 (4): 244-53. https://doi.org/10.32323/ujma.407774.
EndNote
Hamdi Cherif M, Ziane D (December 1, 2018) Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations. Universal Journal of Mathematics and Applications 1 4 244–253.
IEEE
[1]M. Hamdi Cherif and D. Ziane, “Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations”, Univ. J. Math. Appl., vol. 1, no. 4, pp. 244–253, Dec. 2018, doi: 10.32323/ujma.407774.
ISNAD
Hamdi Cherif, Mountassir - Ziane, Djelloul. “Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations”. Universal Journal of Mathematics and Applications 1/4 (December 1, 2018): 244-253. https://doi.org/10.32323/ujma.407774.
JAMA
1.Hamdi Cherif M, Ziane D. Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations. Univ. J. Math. Appl. 2018;1:244–253.
MLA
Hamdi Cherif, Mountassir, and Djelloul Ziane. “Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations”. Universal Journal of Mathematics and Applications, vol. 1, no. 4, Dec. 2018, pp. 244-53, doi:10.32323/ujma.407774.
Vancouver
1.Mountassir Hamdi Cherif, Djelloul Ziane. Homotopy Analysis Aboodh Transform Method for Nonlinear System of Partial Differential Equations. Univ. J. Math. Appl. 2018 Dec. 1;1(4):244-53. doi:10.32323/ujma.407774