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New Development of Variational Iteration Method Using Quasilinearization Method for Solving Nonlinear Problems

Author

Listed:
  • Vikash Kumar Sinha

    (Department of Mathematics, School of Advanced Sciences, VIT AP University, Amaravati 522237, Andhra Pradesh, India)

  • Prashanth Maroju

    (Department of Mathematics, School of Advanced Sciences, VIT AP University, Amaravati 522237, Andhra Pradesh, India)

Abstract

In this paper, we developed a new variational iteration method using the quasilinearization method and Adomian polynomial to solve nonlinear differential equations. The convergence analysis of our new method is also discussed under the Lipschitz continuity condition in Banach space. Some application problems are included to test the efficacy of our proposed method. The behavior of the method is investigated for different values of parameter t. This is a powerful technique for solving a large number of nonlinear problems. Comparisons of our technique were made with the available exact solution and existing methods to examine the applicability and efficiency of our approach. The outcome revealed that the proposed method is easy to apply and converges to the solution very fast.

Suggested Citation

  • Vikash Kumar Sinha & Prashanth Maroju, 2023. "New Development of Variational Iteration Method Using Quasilinearization Method for Solving Nonlinear Problems," Mathematics, MDPI, vol. 11(4), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:935-:d:1066051
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    References listed on IDEAS

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    1. Singh, Randhir & Guleria, Vandana & Singh, Mehakpreet, 2020. "Haar wavelet quasilinearization method for numerical solution of Emden–Fowler type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 123-133.
    2. Eman S. Alaidarous & Malik Zaka Ullah & Fayyaz Ahmad & A.S. Al-Fhaid, 2013. "An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, November.
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