An effective method in investigating structures of polytropic protoplanets formed via gravitational instability.

In this article, we have reinvestigated the initial distribution of thermodynamic variables inside the protoplanets formed via gravitational instability having mass range 0.3 - 10 M J ( 1 M J = 1.8986 × 10 30  gm ) by an embedded RKACeM(4,4) method assuming that the polytropic gas law holds in the protoplanets. The findings attained by our numerical experiments are recognized to be consistent with the results acquired through other notable investigations in this regard. Furthermore, the model is easily computable. The used method is found to be efficient in investing the structures of polytropic protoplanets in their initial stages in terms of accuracy, stability, computational cost, and solving endpoint constraints.

Solving protoplanetary structure equations using Adomian decomposition method.

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 × 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.