Application of new RKAHeM(4,4) technique to analyze the structure of initial extrasolar giant protoplanets

作者：Senthilkumar Sukumar^*; Paul Gour Chandra

来源：Earth Science Informatics, 2012, 5(1): 23-31.

DOI：10.1007/s12145-011-0093-4

• Convective
• Instability
• Runge-Kutta method
• New RKAHeM(4,4) technique
• Truncation errors
• Error estimates

Establishing and successfully implementing new 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 newly proposed simple embedded RKAHeM(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 masses. The case of convection is a significant concern for transference of heat inside the protoplanet and the graphical solution demonstrates positively better performance by inducting the newly proposed effective RKAHeM(4,4) algorithm for any length of time in comparison with the results through Classical Runge-Kutta method. Furthermore, the analytic expression for local truncation error, global truncation error and error estimates are derived for better understanding. A viable quantitative analysis has been carried out to clearly visualize the goodness and robustness of the proposed RKAHeM(4,4) algorithm.

• 出版日期2012-3