Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method
by
Huda O. Bakodah 1,2 and Abdelhalim Ebaid 3,*
Huda O. Bakodah 1,2 and Abdelhalim Ebaid 3,*
1
Department of Mathematics, Faculty of Science-AL Faisaliah Campus, King Abdulaziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia
2
Mathematics Department, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
3
Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
*
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.
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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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