Numerical computation of nonlinear shock wave equation of fractional order

被引:40
|
作者
Kumar, Devendra [1 ]
Singh, Jagdev [2 ]
Kumar, Sunil [3 ]
Sushila [4 ]
Singh, B. P. [5 ]
机构
[1] JECRC Univ, Dept Math, Jaipur 303905, Rajasthan, India
[2] Jagan Nath Univ, Dept Math, Jaipur 303901, Rajasthan, India
[3] Natl Inst Technol, Dept Math, Jamshedpur 831014, Jharkhand, India
[4] Yagyavalkya Inst Technol, Dept Phys, Jaipur 302022, Rajasthan, India
[5] IEC Coll Engn & Technol, Dept Math, Greater Noida 201306, Uttar Pradesh, India
关键词
Laplace transform method; Homotopy analysis method; Homotopy analysis transform method; Maple code; Fractional nonlinear shock wave equation;
D O I
10.1016/j.asej.2014.10.015
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The main aim of the present paper was to present a user friendly approach based on homotopy analysis transform method to solve a time-fractional nonlinear shock wave equation arising in the flow of gases. The proposed technique presents a procedure of constructing the set of base functions and gives the high-order deformation equations in a simple form. The auxiliary parameter /in the homotopy analysis transform method solutions has provided a convenient way of controlling the convergence region of series solutions. The method is not limited to the small parameter, such as in the classical perturbation method. The technique gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained by the proposed approach indicate that the approach is easy to implement and computationally very attractive. (C) 2014 Production and hosting by Elsevier B. V. on behalf of Ain Shams University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
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页码:605 / 611
页数:7
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