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

Abstract

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.

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Acknowledgements

The first author would like to extend his sincere gratitude to Government of India, eternally for providing financial support during doctoral studies via Technical Quality Improvement Programme (TEQIP), Under Ministry of Human Resource Development, to National Institute of Technology [REC], Tiruchirappalli-620 015, Tamilnadu, India. URL:http://www.nitt.edu. Further, the author expresses his grateful thanks to Government of Malaysia for offering financial grants during post doctoral fellow scheme to Universiti Sains Malaysia [An Apex Public University by Government of Malaysia], School of Mathematical Sciences, Pulau Pinang-11800, Penang, Malaysia. URL:http://www.usm.my. The second author wishes to thank Professor Shishir Kumer Bhattacharjee, Department of Mathematics, University of Rajshahi, for discussions during the time this manuscript was being prepared. The authors also would like to thank the anonymous referees for comments and suggestions that helped us to improve the quality of the manuscript.

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Correspondence to Sukumar Senthilkumar.

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Communicated by: H. A. Babaie

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Senthilkumar, S., Paul, G.C. Application of new RKAHeM(4,4) technique to analyze the structure of initial extrasolar giant protoplanets. Earth Sci Inform 5, 23–31 (2012). https://doi.org/10.1007/s12145-011-0093-4

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Keywords

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