Numerical Runge- Kutta (4, 4) Method to determine the Initial Configurations of the Jupitar Proto Planet Formed Via Disk Instability

M. S.Ali, M.A A.Mamun, M. M. Rahman, R. R. Mondal

Abstract


Numerical computational technique(s) with simulation tool is one of the most important difficult tasks in order to carry out real time scientific astronomical and other sophisticated problems. The main focus and highlight of this paper is concerned with the introduction of a method Runge-Kutta (4, 4) technique to determine the distribution of thermodynamic variables inside protoplanets during pre-collapse stage, formed by gravitational instability, for protoplanetary masses between 0.3 to 10 Jupiter. The case of convection is a significant concern for transference of heat inside the protoplanets and the graphical solution demonstrates positively better performance by the RK (4, 4) algorithm for any length of time. A viable quantitative analysis has been carried out to clearly visualize the goodness and robustness of the Runge-Kutta (4, 4) algorithm.


Keywords


Runge- Kutta (4, 4) Algorithm; Jupitar Protoplanet; Schwarzschild transformations; Clapeyron Equation; Disk Instability Models.

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