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Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm

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  • Ahmad, Hijaz
  • Seadawy, Aly R.
  • Khan, Tufail A.

Abstract

In this paper, we propose an incredible modification of variational iteration algorithm-II that will accelerate the fast convergence of the series solution. We utilize the proposed algorithm on KdV, mKdV and combined KdV–mKdV equations to illustrate its accuracy and reliability. The consequences of modified variational iteration algorithm-II (MVIA-II) show that the proposed technique minimizes the size of calculations, converges rapidly, computationally efficient and yields accurate results. This modification demonstrated the high efficiency and attained very good agreement in illustrated models and might be promptly reached out to other nonlinear PDEs.

Suggested Citation

  • Ahmad, Hijaz & Seadawy, Aly R. & Khan, Tufail A., 2020. "Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 13-23.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:13-23
    DOI: 10.1016/j.matcom.2020.04.005
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    References listed on IDEAS

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    1. Nagatani, Takashi, 1999. "TDGL and MKdV equations for jamming transition in the lattice models of traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 581-592.
    2. Seadawy, Aly R. & Lu, Dianchen & Nasreen, Naila & Nasreen, Shamila, 2019. "Structure of optical solitons of resonant Schrödinger equation with quadratic cubic nonlinearity and modulation instability analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    3. A. R. Seadawy & K. El-Rashidy, 2015. "Classification of Multiply Travelling Wave Solutions for Coupled Burgers, Combined KdV-Modified KdV, and Schrödinger-KdV Equations," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-7, March.
    4. Seadawy, Aly R. & Cheemaa, Nadia, 2019. "Propagation of nonlinear complex waves for the coupled nonlinear Schrödinger Equations in two core optical fibers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 529(C).
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    Cited by:

    1. Asıf Yokus & Hülya Durur & Hijaz Ahmad & Shao-Wen Yao, 2020. "Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
    2. Tomar, Saurabh & Singh, Mehakpreet & Vajravelu, Kuppalapalle & Ramos, Higinio, 2023. "Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 640-644.
    3. Fardi, Mojtaba & Khan, Yasir, 2021. "A novel finite difference-spectral method for fractal mobile/immobiletransport model based on Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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