AUTHOR(S): Melike Ebru Kirkin, Metin Demiralp

TITLE A Case Study on Squarification in Probabilistic Evolution Theory (PREVTH) for HenonHeiles Systems 
ABSTRACT The Probabilistic Evolution Theory (PREVTH) has been effectively developed in recent few years to solve the explicit autonomous ODE(s) accompanied by certain initial conditions. The theory focuses on the cases where right hand side functions are conical in unknowns at the right hand side. If it is not so certain space extension technies are used to get conicality. [1–6]. Theory gives an analytical Kronecker power series solution almost for all practically encountered systems. The squarification reduces the enormous sparsity and gets very high efficiency. This work is designed for the application of PREVTH Squarification on HenonHeiles systems as a case study. 
KEYWORDS Ordinary differential equation, probabilistic evolution theory, HenonHeiles, squarification 
REFERENCES [1] M. Demiralp, “Squarificating the Telescope Matrix Images of Initial Value Vector in Probabilistic Evolution Theory (PET),” in Proceedings of the 19th International Conference on Applied Mathematics (AMATH14), ISBN: 978161804 2583, WSEAS Press, ˙Istanbul, Turkiye, 2014, ¨ pp. 99104. [2] M. E. Kırkın, and C. Goz¨ ukırmızı, “Probabilis ¨ tic Evolution Theory for ODE Sets with Second Degree Multinomial Right Hand Side Functions: Certain Reductive Cases”ICCMSE, Atina, Greece, 2015. [3] C. Goz¨ ukırmızı, “Probabilistic Evolution The ¨ ory for ODE Sets with Second Degree Multinomial Right Hand Side Functions: Implementation” ICCMSE, Atina, Greece, 2015. [4] C. Goz¨ ukırmızı,“Sıradan T ¨ urevli Denklemlerin ¨ Olasılıksal Evriminin ˙Izgesel Niteliklerinde Yoney ve Katlıdizi Tabanlı ¨ ˙Incelemeler”, PhD Thesis, in Turkish, Informatics Institute, ˙Istanbul Technical University, 2015. [5] C. Goz¨ ukırmızı, and M. Demiralp, ¨ Journal of Mathematical Chemistry, 52, 866880 (2014), ISSN 02599791, URL http://dx.doi. org/10.1007/s1091001302985 [6] C. Goz¨ ukırmızı, and M. Demiralp, ¨ Journal of Mathematical Chemistry, 52, 881898 (2014), ISSN 02599791, URL http://dx.doi. org/10.1007/s1091001302994 
Cite this paper Melike Ebru Kirkin, Metin Demiralp. (2016) A Case Study on Squarification in Probabilistic Evolution Theory (PREVTH) for HenonHeiles Systems. International Journal of Computers, 1, 158165 
