Numerical Solution of Time Fractional Gas Dynamics Equation

  • Authors

    • T. R.Ramesh Rao
    • R. Santosh Balaji
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.21294
  • Gas Dynamics equation, Laplace-Adomian decomposition method, Fractional derivative, Fractional complex transform.
  • Abstract

    In this paper, we propose new technique for solving time fractional gas dynamics equation using Laplace-Adomian Decomposition method coupled with fractional complex transform. It is found that the tested examples reveal the present method is more reliable and does not require strong assumptions.

     

     

  • References

    1. [1] Evans DJ & Bulut H (2002), A new approach to the gas dynamics equation: An application of the decomposition method, International Journal of Computer Mathematics 79, 817-822.

      [2] Elizarova TG (2009), Quasi-gas dynamics equations, ISBN: 978-3-642-00291-5, Springer Verlag.

      [3] Aminikhah H & Ali Jamalian (2013), Numerical Approximation for Nonlinear Gas Dynamic Equation, International Journal of Partial Differential Equations, http://dx.doi.org/10.1155/2013/846749

      [4] Das S & Kumar R (2011), Approximate analytical solutions of fractional gas dynamics equations, Applied Mathematics and Computation 217, 9905-9915.

      [5] Sunil Kumar, Mohammad Mehdi Rashidi, Deepak Kumar & Navid Freidoonimehr (2014), New analytical method for gas dynamics equation arising in shock fronts, Computer Physics Communications, http://dx.doi.org/10.1016/j.cpc.2014.03.025.

      [6] Mohammed Tamsir & Vineet K. Srivastava (2016), Revisiting the approximate analytical solution of fractional-order gas dynamics equation, Alexandria Engineering Journal 55, 867-874.

      [7] Sunil Kumar, HuseyinKocak & AhmetYıldırım (2012), A Fractional Model of Gas Dynamics Equations and its Analytical Approximate Solution Using Laplace Transform, Verlag der Zeitschrift fur Naturforschung 67, 389-396.

      [8] Jagadev Singh, Devendra Kumar & Kilicman A (2013), Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform, Abstract and Applied Analysis, http://dx.doi.org/10.1155/2013/934060

      [9] Jafari H, Chun C, Seifi S & Saeidy M (2009), Analytical solution for nonlinear gas dynamics equation by homotopy analysis method, Appl.Appl.Math..4, 149-154.

      [10] Ongun MY(2011), The Laplace Adomian decomposition method for solving a model for HIV infection of CD4+ T cells, Mathematical and Computer Modeling 53,597-603.

      [11] NurettinDogan (2012), Numerical treatment of the model for HIV infection of CD4+ Tcells by using multistep Laplace Adomian Decomposition method, Discrete Dynamics in nature and Society, http://dx.doi.org/10.1155/2012/976352

      [12] Susmita Paul, Sankar Prasad Mondal & Paritosh Battacharya (2016), Numerical solution of Lokta-Volterra Prey Predator Model Runge-Kutta Felhberg method and Laplace Adomian Decomposition method, Alexandria Engineering Journal 55, 613-617.

      [13] Abdul-MajidWazwaz (2010), The combined Laplace transform- Adomian Decomposition method for handling Volterraintegro-differential equations, Applied Mathematics and Computation 216, 1304-1309.

      [14] Jafari M, Khalique CM & Nazari M (2011), Application of the Laplace decomposition method method for solving linear and nonlinear fractional diffusion-wave equations, Applied Mathematics Letters 24, 1799-1805.

      [15] Arunkumar & Ram Dayal Pankaj (2012), Laplace Decomposition method to study wave solutions of coupled nonlinear partial differential equation, Computational Mathematics, Article ID 423469.

      [16] Khuri SA (2001), A Laplace decomposition algorithm applied to class of nonlinear differential equations, J. Math. Appl. 4, 141-155.

      [17] Ramesh Rao T R (2017), Numerical solution for time fractional gas dynamics equations through reduced differential transform method coupled with fractional complex transform, International Journal of Pure and Applied Mathematics 117, 111-118.

      [18] Ji-Huan He, Elagan SK & Li ZB (2012), Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus, Physics Letters A 376, 257-259.

      [19] Guy Jumarie (2007), Fractional partial differential equations and modified Riemann-Liuville derivatives new methods for solution, J.Appl.Math.& Comp. 24, 31-48.

      [20] Zeng Biao Li & Ji-Juan He (2010), Fractional complex transform for fractional differential equation, Mathematical and Computational Applications 15, 970-973.

      [21] Saha Ray S & Sahoo S (2015), A Novel Analytical Method with fractional complex transform for new exact solutions of time-fractional fifth-order Swada-Kotera Equation, Reports on Mathematical Physics 75, 65-72.

      [22] Zeng Biao Li & Ji-Juan He (2010), Fractional complex transform for fractional differential equation, Mathematical and Computational Applications 15, 970-973.

      [23] Hossein Aminihkah & Ali Jamalian (2013), Numerical Approximation for Nonlinear Gas Dynamics Equations, International Journal of Partial differential Equations, http://dx.doi.org/10.1155/2013/846749.

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  • How to Cite

    R.Ramesh Rao, T., & Santosh Balaji, R. (2018). Numerical Solution of Time Fractional Gas Dynamics Equation. International Journal of Engineering & Technology, 7(4.10), 610-612. https://doi.org/10.14419/ijet.v7i4.10.21294

    Received date: 2018-10-08

    Accepted date: 2018-10-08

    Published date: 2018-10-02