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Z. Naturforsch. 67a, 389 – 396
(2012)
doi:10.5560/ZNA.2012-0038
A Fractional Model of Gas Dynamics Equations and its Analytical Approximate Solution Using Laplace Transform
1 Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, Jharkhand, India
2 Department of Mathematical Sciences, University of Bath, Bath BA, United Kingdom
3 Department of Applied Mathematics, Faculty of Science, Ege University, Bornova, Izmir, Turkey
Received November 30, 2011 / revised April 4, 2012 / published online July 3, 2012
Reprint requests to: S. K.; E-mail:
skiitbhu28@gmail.com
In this study, the homotopy perturbation transform method (HPTM) is performed to give approximate and analytical solutions of nonlinear homogenous and non-homogenous time-fractional gas dynamics equations. Gas dynamics equations are based on the physical laws of conservation, namely, the laws of conservation of mass, conservation of momentum, conservation of energy etc. The HPTM is a combined form of the Laplace transform, the homotopy perturbation method, and He's polynomials. The nonlinear terms can be easily handled by the use of He's polynomials. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. Some numerical illustrations are given. These results reveal that the proposed method is very effective and simple to perform.
Key words: Homotopy Perturbation Method; Laplace Transform; Gas Dynamics Equation; Analytical Solution.
Mathematics Subject Classification 2000: 26A33; 34A08; 34A34