Finding the Exact Solution of Special Nonlinear Partial Differential Equations by Homotopy Analysis Method

Authors

  • Mashallah MATINFAR Department of Mathematics and Computer Science, University of Mazandaran, Babolsar
  • Mohammad SAEIDY Department of Mathematics and Computer Science, University of Mazandaran, Babolsar
  • Yasir KHAN Department of Mathematics, Zhejiang University, Hangzhou 310027
  • Behzad GHARAHSUFLU Department of Mathematics, Islamic Azad University Qaemshahr Branch, Qaemshahr

Keywords:

Homotopy analysis method, nonlinear parabolic-hyperbolic partial differential equations

Abstract

In this paper, the homotopy analysis method was used to solve nonlinear parabolic-hyperbolic partial differential equations. Examples are presented here to show the usability of the method for such equations. The results show that the HAM is very effective and convenient and that the obtained solutions of HAM have high accuracy.

doi:10.14456/WJST.2014.36

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References

SJ Liao. 1992, The proposed homotopy analysis technique for the solution of nonlinear problems. Ph.D. Thesis, Shanghai Jiao Tong University, China.

SJ Liao. Beyond Perturbation: Introduction to the Homotopy Analysis Method. CRC Press, Boca Raton, 2003.

SJ Liao. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 2004; 147, 499-513.

M Saeidy, M Matinfar and J Vahidi. Analytical solution of BVPs for fourth-order integro-differential equations by using homotopy analysis method. Int. J. Nonlinear Sci. 2010; 9, 414-21.

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JH He. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Nonlinear Mech. 2000; 35, 37-43.

M Matinfar and M Saeidy. The homotopy perturbation method for solving higher dimensional initial boundary value problems of variable coefficients. World J. Model. Simulat. 2009; 9, 72-80.

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Published

2013-10-31

How to Cite

MATINFAR, M., SAEIDY, M., KHAN, Y., & GHARAHSUFLU, B. (2013). Finding the Exact Solution of Special Nonlinear Partial Differential Equations by Homotopy Analysis Method. Walailak Journal of Science and Technology (WJST), 11(3), 171–178. Retrieved from https://wjst.wu.ac.th/index.php/wjst/article/view/310