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Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method

Author

Listed:
  • Huda O. Bakodah

    (Department of Mathematics, Faculty of Science-AL Faisaliah Campus, King Abdulaziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia
    Mathematics Department, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

  • Abdelhalim Ebaid

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

Abstract

The Ambartsumian equation, a linear differential equation involving a proportional delay term, is used in the theory of surface brightness in the Milky Way. In this paper, the Laplace-transform was first applied to this equation, and then the decomposition method was implemented to establish a closed-form solution. The present closed-form solution is reported for the first time for the Ambartsumian equation. Numerically, the calculations have demonstrated a rapid rate of convergence of the obtained approximate solutions, which are displayed in several graphs. It has also been shown that only a few terms of the new approximate solution were sufficient to achieve extremely accurate numerical results. Furthermore, comparisons of the present results with the existing methods in the literature were introduced.

Suggested Citation

  • Huda O. Bakodah & Abdelhalim Ebaid, 2018. "Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method," Mathematics, MDPI, vol. 6(12), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:331-:d:191047
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    Citations

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    Cited by:

    1. Aneefah H. S. Alenazy & Abdelhalim Ebaid & Ebrahem A. Algehyne & Hind K. Al-Jeaid, 2022. "Advanced Study on the Delay Differential Equation y ′( t ) = ay ( t ) + by ( ct )," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
    2. Reem Alrebdi & Hind K. Al-Jeaid, 2023. "Accurate Solution for the Pantograph Delay Differential Equation via Laplace Transform," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    3. Abdulrahman B. Albidah, 2023. "A Proposed Analytical and Numerical Treatment for the Nonlinear SIR Model via a Hybrid Approach," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    4. Abdulrahman B. Albidah & Nourah E. Kanaan & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2023. "Exact and Numerical Analysis of the Pantograph Delay Differential Equation via the Homotopy Perturbation Method," Mathematics, MDPI, vol. 11(4), pages 1-14, February.

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