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The residual power series method for the one-dimensional unsteady flow of a van der Waals gas

Author

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  • Az-Zo’bi, Emad A.
  • Yıldırım, Ahmet
  • AlZoubi, Wael A.

Abstract

A residual power series scheme is developed for mixed-type p-system of conservation laws. The residual power series method (RPSM) does not require discretization, reduces the system to an explicit system of algebraic equations and consequently of massive computations. Convergence hypotheses are discussed and error bounds of exponential rates are derived. The scheme is numerically tested to several cases of the van der Waals equations which arise in fluid dynamics. Stability is obtained graphically while transition through regions. The reported results reveal the reliability, efficiency and economical implementation of the proposed algorithm for handling nonlinear partial differential equations in applied mathematics.

Suggested Citation

  • Az-Zo’bi, Emad A. & Yıldırım, Ahmet & AlZoubi, Wael A., 2019. "The residual power series method for the one-dimensional unsteady flow of a van der Waals gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 188-196.
    • Handle: RePEc:eee:phsmap:v:517:y:2019:i:c:p:188-196
    DOI: 10.1016/j.physa.2018.11.030
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    References listed on IDEAS

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    1. Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, July.
    2. Anas Arafa & Ghada Elmahdy, 2018. "Application of Residual Power Series Method to Fractional Coupled Physical Equations Arising in Fluids Flow," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-10, July.
    3. Az-Zo'bi, Emad A. & Dawoud, Kamal Al & Marashdeh, Mohammad, 2015. "Numeric-analytic solutions of mixed-type systems of balance laws," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 133-143.
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    Cited by:

    1. Emad A. Az-Zo’bi & Kamel Al-Khaled & Amer Darweesh, 2019. "Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method," Mathematics, MDPI, vol. 7(6), pages 1-13, June.
    2. Zhao, Dazhi & Yu, Guozhu & Tian, Yan, 2020. "Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.

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