Solving protoplanetary structure equations using Adomian decomposition method

Gour Chandra Paul; Shahinur Khatun; Md Nuruzzaman; Dipankar Kumar; Md Emran Ali; Farjana Bilkis; Mrinal Chandra Barman

doi:10.1016/j.heliyon.2021.e08213

Solving protoplanetary structure equations using Adomian decomposition method

Heliyon. 2021 Oct 20;7(10):e08213. doi: 10.1016/j.heliyon.2021.e08213. eCollection 2021 Oct.

Authors

Gour Chandra Paul¹, Shahinur Khatun¹, Md Nuruzzaman², Dipankar Kumar³, Md Emran Ali^{1

4}, Farjana Bilkis⁵, Mrinal Chandra Barman^{1

6}

Affiliations

¹ Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh.
² Department of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi 6204, Bangladesh.
³ Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj 8100, Bangladesh.
⁴ Department of Textile Engineering, Northern University Bangladesh, Dhaka 1230, Bangladesh.
⁵ Department of Science and Humanities, Bangladesh Army International University of Science and Technology, Cumilla 3501, Bangladesh.
⁶ Department of Mathematics, Mawlana Bhashani Science and Technology University, Tangail 1902, Bangladesh.

Abstract

In this paper, the distribution of thermodynamic variables in the protoplanets formed by gravitational instability in the mass range $0.3 - 10 M_{J}$ ( $1 M_{J} = 1$ Jupiter mass = $1.8986 \times 10^{30}$ gm) is investigated in their initial state by solving the structure equations via the Adomian decomposition method. Concerning the heat transfer in the protoplanets, the mode of convection is taken into account. The outcomes indicate that there is a reasonably good agreement between the Adomian semi-analytical solution containing only first 8 terms and the numerical results.

Keywords: Adomian decomposition method; Disk instability; Protoplanet; Thermodynamic variables.