Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions. The first solution is provided i...

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Bibliographic Details
Published in:Mathematical and computational applications 2019-03, Vol.24 (1), p.7
Main Authors: Ebaid, Abdelhalim, Al-Enazi, Asmaa, Albalawi, Bassam Z., Aljoufi, Mona D.
Format: Article
Language:English
Subjects:
Adomian decomposition method
Ambartsumian equation
Milky way
series solution
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Summary:The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions. The first solution is provided in the form of a power series which agrees with the solution in the literature, while the second expresses the solution in terms of exponential functions which is viewed as a new solution. A rapid rate of convergence has been achieved and displayed in several graphs. Furthermore, only a few terms of the new approximate solution (expressed in terms of exponential functions) are sufficient to achieve extremely accurate numerical results when compared with a large number of terms of the first solution in the literature. In addition, the residual error using a few terms approaches zero as the delay parameter increases, hence, this confirms the effectiveness of the present approach over the solution in the literature.
ISSN:2297-8747
2297-8747
DOI:10.3390/mca24010007