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A New Fractional Model of Nonlinear Shock Wave Equation Arising in Flow of Gases

A New Fractional Model of Nonlinear Shock Wave Equation Arising in Flow of Gases AbstractIn this paper, we present a numerical algorithmbased on new homotopy perturbation transform method(HPTM) to solve a time-fractional nonlinear shock waveequation which describes the flow of gases. The fractionalderivative is considered in the Caputo sense. The HPTM iscombined form of Laplace transform, homotopy perturbationmethod and He’s polynomials. The nonlinear termscan be easily handled by the use of He’s polynomials. Thetechnique finds the solution without any discretization orrestrictive assumptions and avoids the round-off errors.The obtained results are in good agreement with the existingones in open literature and it is shown that the techniqueintroduced here is robust, efficient, easy to implementand computationally very attractive. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

A New Fractional Model of Nonlinear Shock Wave Equation Arising in Flow of Gases

Nonlinear Engineering , Volume 3 (1): 8 – Mar 1, 2014

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References (52)

Publisher
de Gruyter
Copyright
© 2014 by Walter de Gruyter GmbH & Co.
ISSN
2192-8029
eISSN
2192-8029
DOI
10.1515/nleng-2013-0022
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper, we present a numerical algorithmbased on new homotopy perturbation transform method(HPTM) to solve a time-fractional nonlinear shock waveequation which describes the flow of gases. The fractionalderivative is considered in the Caputo sense. The HPTM iscombined form of Laplace transform, homotopy perturbationmethod and He’s polynomials. The nonlinear termscan be easily handled by the use of He’s polynomials. Thetechnique finds the solution without any discretization orrestrictive assumptions and avoids the round-off errors.The obtained results are in good agreement with the existingones in open literature and it is shown that the techniqueintroduced here is robust, efficient, easy to implementand computationally very attractive.

Journal

Nonlinear Engineeringde Gruyter

Published: Mar 1, 2014

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