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On Analytical Solution of Ambartsumian Equation

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Abstract

The Ambartsumian equation is used in the theory of surface brightness in milky way. This equation is a linear differential equation involving a proportional delay term. In this paper we use the Daftardar-Gejji and Jafari method to obtain analytical solution of Ambartsumian equation. The solution is provided in the form of a power series which is convergent for all reals. We prove the convergence of this series and plot solution graphs.

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Acknowledgements

The authors acknowledge NBHM, Department of Atomic Energy Mumbai, India for funding through Research Project [2148(6)/2013/NBHM(R.P.)/R & D II/689] and CSIR, New Delhi for funding through Research Project [25(0245)/15/EMR-II].

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Authors and Affiliations

  1. Department of Mathematics, Shivaji University, Kolhapur, 416004, India

    Jayvant Patade & Sachin Bhalekar

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  1. Jayvant Patade
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  2. Sachin Bhalekar
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Correspondence to Jayvant Patade.

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Patade, J., Bhalekar, S. On Analytical Solution of Ambartsumian Equation. Natl. Acad. Sci. Lett. 40, 291–293 (2017). https://doi.org/10.1007/s40009-017-0565-2

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  • DOI: https://doi.org/10.1007/s40009-017-0565-2

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