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

Huda O. Bakodah and Abdelhalim Ebaid
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Huda O. Bakodah: Department of Mathematics, Faculty of Science-AL Faisaliah Campus, King Abdulaziz University, P.O. Box 80200, Jeddah 21589, Saudi Arabia
Abdelhalim Ebaid: Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia

Mathematics, 2018, vol. 6, issue 12, 1-10

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.

Keywords: Adomian decomposition method; Ambartsumian equation; Laplace-transform; analytic solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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