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

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Department of Mathematics, Faculty of Science-AL Faisaliah Campus, King Abdulaziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia
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Mathematics Department, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
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Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
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Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 331; https://doi.org/10.3390/math6120331
Received: 13 November 2018 / Revised: 7 December 2018 / Accepted: 11 December 2018 / Published: 17 December 2018
(This article belongs to the Section Engineering Mathematics)
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. View Full-Text
Keywords: Adomian decomposition method; Ambartsumian equation; Laplace-transform; analytic solution Adomian decomposition method; Ambartsumian equation; Laplace-transform; analytic solution
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MDPI and ACS Style

Bakodah, H.O.; Ebaid, A. Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method. Mathematics 2018, 6, 331.

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