Abstract
The main motivation and novel notion of this present communication is to implement the recently suggested fourth order with four stages embedded RKARMS(4,4) algorithm to examine its efficiency in reinvesting the structures of extrasolar protoplanets formed via disk instability which being presented in Paul et al. [1] (G.C. Paul, M.M. Rahman, D. Kumar, M.C. Barman, the radius spectrum of solid grains settling in gaseous giant protoplanets, Earth Sci. Inform. 6 (2013) 137-144) for the case of convective heat transfer using classical Runge-Kutta (RK) technique of order four. The results by the RKARMS(4,4) algorithm compared well with those obtained by the classical RK method of order four for any time length and found to be more suitable.