Execution of novel explicit RKARMS(4,4) technique in determining initial configurations of extra-solar protoplanets formed by disk instability

Implementation of a novel embedded Runge–Kutta fourth order four stage arithmetic root mean square technique to determine initial configurations of extra-solar protoplanets formed by gravitational instability is the main goal of this present paper. A general mathematical framework for the introduced numerical technique is described in addition to error estimation description. It is noticed that the numerical outputs through the employed novel RKARMS(4,4) method are found to be more effective and efficient in comparison with the results obtained by the classical Runge–Kutta technique.