Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 7 (2012), 105 -- 116


V.G. Gupta and Sumit Gupta

Abstract. In this paper, by means of the homotopy analysis method (HAM), the solutions of some nonlinear Cauchy problem of parabolic-hyperbolic type are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter \hbar that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.

2010 Mathematics Subject Classification: 58B05; 49Mxx.
Keywords: Homotopy analysis method; nonlinear cauchy's problem; exact solution; Homotopy perturbation method

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V.G. Gupta
Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, India.
Sumit Gupta
University of Rajasthan, Jaipur, Rajasthan, India. e-mail:
JaganNath Gupta Institute of Engineering and Technology, Sitapura, Jaipur, Rajasthan, India.