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Numeric-analytic solutions of mixed-type systems of balance laws

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  • Az-Zo'bi, Emad A.
  • Dawoud, Kamal Al
  • Marashdeh, Mohammad

Abstract

The aim of the present analysis is to apply two relatively recent methods, reduced differential transform method (RDTM) and differential transform method (DTM), for the solution of balance law systems. New generalized transformed formulas are derived. The new approaches provided the solution in the form of a rapidly convergent series with easily computable components in the RDTM case, and costly components for the DTM. A comparison between the two methodologies shows that the RDTM is more effective, efficient, powerful and able to be applicable for large class of nonlinear partial differential equations than the DTM. Two test modeling problems are discussed to illustrate the effectiveness and performance of RDTM.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:133-143
    DOI: 10.1016/j.amc.2015.04.119
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    References listed on IDEAS

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    1. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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    Cited by:

    1. Noha M. Rasheed & Mohammed O. Al-Amr & Emad A. Az-Zo’bi & Mohammad A. Tashtoush & Lanre Akinyemi, 2021. "Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
    2. 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.
    3. 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.

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