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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Article
New Analytic Solution for Ambartsumian Equation
Author(s)
Fahad M. Alharbi and Abdelhalim Ebaid
Full-Text PDF
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DOI:doi: 10.17265/2159-5291/2018.07.002
Affiliation(s)
Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
ABSTRACT
Analytical solution is obtained for Ambartsumian equation in this paper. This equation is of application in astronomy. The obtained solution has many advantages over the published one in the literature as shown by several comparisons.
KEYWORDS
Delay equation, analytic solution.
Cite this paper
Alharbi F. M., and Ebaid A. 2018. "New Analytic Solution for Ambartsumian Equation." Journal of Mathematics and System Science 8 (2018): 182-6.
References
[1] Patade, J., and Bhalekar, S. 2017. “On Analytical Solution of Ambartsumian Equation.” Natl. Acad. Sci. Lett. 40 (4): 291-3. DOI 10.1007/s40009-017-0565-2.
[2] Ambartsumian, V. A. 1994. “On the Fluctuation of the Brightness of the Milky Way.” Doklady Akad Nauk USSR 44: 223-6.
[3] Kato, T., and McLeod, J. B. 1971. “The Functional-Differential Equation y'(x) = ay(λx)+by(x).” Bull. Am. Math. Soc. 77: 891-935.
[4] Daftardar-Gejji, V., and Bhalekar, S. 2008. “Solving Fractional Diffusion-Wave Equations Using the New Iterative Method.” Fract. Calc. Appl. Anal. 11: 193-202.
[5] Adomian, G., and Rach, R. 1985. “On the Solution of Algebraic Equations by the Decomposition Method.” J. Math. Anal. Applic. 105: 141-66.
[6] Adomian, G., and Rach, R. 1985. “Algebraic Equations with Exponential Terms.” J. Math. Anal. Applic. 112 (1): 136-40.
[7] Wazwaz, A. M. 2005. “Adomian Decomposition Method for a Reliable Treatment of the Bratu-Type Equations.” Appl. Math. Comput. 166: 652-63.
[8] Wazwaz, A. M. 2010. “The Combined Laplace Transform-Adomian Decomposition Method for Handling Nonlinear Volterra Integro-Differential Equations.” Appl. Math. Comput. 216: 1304-9.
[9] Alshaery, A., and Ebaid, A. 2017. “Accurate Analytical Periodic Solution of the Elliptical Kepler Equation Using the Adomian Decomposition Method.” Acta Astronautica 140: 27-33.
[10] Patra, A., and Saha Ray, S. 2014. “Homotopy Perturbation Sumudu Transform Method for Solving Convective Radial Fins with Temperature-Dependent Thermal Conductivity of Fractional Order Energy Balance Equation.” International Journal of Heat and Mass Transfer 76: 162-70.
[11] Ayati, Z., and Biazar, J. 2014. “On the Convergence of Homotopy Perturbation Method.” Journal of the Egyptian Mathematical Society 23: 424-8. http://dx.doi.org/10.1016/j.joems.2014.06.015.
[12] Alshaery, A. 2017. “The Homotopy Perturbation Method for Accurate Orbits of the Planets in the Solar System: The Elliptical Kepler Equation.” Z. Naturforschung A., https://doi.org/10.1515/zna-2017-0181.
[2] Ambartsumian, V. A. 1994. “On the Fluctuation of the Brightness of the Milky Way.” Doklady Akad Nauk USSR 44: 223-6.
[3] Kato, T., and McLeod, J. B. 1971. “The Functional-Differential Equation y'(x) = ay(λx)+by(x).” Bull. Am. Math. Soc. 77: 891-935.
[4] Daftardar-Gejji, V., and Bhalekar, S. 2008. “Solving Fractional Diffusion-Wave Equations Using the New Iterative Method.” Fract. Calc. Appl. Anal. 11: 193-202.
[5] Adomian, G., and Rach, R. 1985. “On the Solution of Algebraic Equations by the Decomposition Method.” J. Math. Anal. Applic. 105: 141-66.
[6] Adomian, G., and Rach, R. 1985. “Algebraic Equations with Exponential Terms.” J. Math. Anal. Applic. 112 (1): 136-40.
[7] Wazwaz, A. M. 2005. “Adomian Decomposition Method for a Reliable Treatment of the Bratu-Type Equations.” Appl. Math. Comput. 166: 652-63.
[8] Wazwaz, A. M. 2010. “The Combined Laplace Transform-Adomian Decomposition Method for Handling Nonlinear Volterra Integro-Differential Equations.” Appl. Math. Comput. 216: 1304-9.
[9] Alshaery, A., and Ebaid, A. 2017. “Accurate Analytical Periodic Solution of the Elliptical Kepler Equation Using the Adomian Decomposition Method.” Acta Astronautica 140: 27-33.
[10] Patra, A., and Saha Ray, S. 2014. “Homotopy Perturbation Sumudu Transform Method for Solving Convective Radial Fins with Temperature-Dependent Thermal Conductivity of Fractional Order Energy Balance Equation.” International Journal of Heat and Mass Transfer 76: 162-70.
[11] Ayati, Z., and Biazar, J. 2014. “On the Convergence of Homotopy Perturbation Method.” Journal of the Egyptian Mathematical Society 23: 424-8. http://dx.doi.org/10.1016/j.joems.2014.06.015.
[12] Alshaery, A. 2017. “The Homotopy Perturbation Method for Accurate Orbits of the Planets in the Solar System: The Elliptical Kepler Equation.” Z. Naturforschung A., https://doi.org/10.1515/zna-2017-0181.