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Solving the Nonlinear Charged Particle Oscillation Equation Using the Laplace–Adomian Decomposition Method

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  • Omar Alomari
  • Bashar F. Garalleh
  • Emad K. Jaradat
  • Behzad Omidi Koma
  • Ivan Giorgio

Abstract

This manuscript presents a comprehensive exploration of the nonlinear charged particle oscillation equation, employing the Laplace–Adomian decomposition method (LDM) to obtain approximate analytical solutions. The investigation leads to the formulation of five initial equations governing the oscillatory behavior of a charged particle, which are visually represented and analyzed with insightful interpretations. Notably, the existing literature lacks an exact solution to this problem. However, this paper fills this gap by presenting an approximate analytical solution utilizing the LDM. The solution is carefully studied and analyzed, contributing to a deeper understanding of the complex behavior of charged particle oscillation.

Suggested Citation

  • Omar Alomari & Bashar F. Garalleh & Emad K. Jaradat & Behzad Omidi Koma & Ivan Giorgio, 2024. "Solving the Nonlinear Charged Particle Oscillation Equation Using the Laplace–Adomian Decomposition Method," Advances in Mathematical Physics, Hindawi, vol. 2024, pages 1-9, October.
    • Handle: RePEc:hin:jnlamp:6066821
    DOI: 10.1155/2024/6066821
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    Cited by:

    1. Chein-Shan Liu & Chung-Lun Kuo & Chih-Wen Chang, 2024. "Decomposition–Linearization–Sequential Homotopy Methods for Nonlinear Differential/Integral Equations," Mathematics, MDPI, vol. 12(22), pages 1-29, November.

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