Approximate solutions of the hyperchaotic R ¨ossler system by using the Bessel collocation scheme

Approximate solutions of the hyperchaotic Rössler system by using the Bessel collocation scheme

The purpose of this study is to give a Bessel polynomial approximation for the solutions of the hyperchaotic R¨ossler system.For this purpose, the Bessel collocation method applied to different problems is developed for the mentioned system. This method isbased on taking the truncated Bessel expansions of the functions in the hyperchaotic R¨ossler systems. The suggested secheme convertsthe problem into a system of nonlinear algebraic equations by means of the matrix operations and collocation points, The accuracy andefficiency of the proposed approach are demonstrated by numerical applications and performed with the help of a computer code writtenin Maple. Also, comparison between our method and the differential transformation method is made with the accuracy of solutions

Keywords:

Hyperchaotic R¨ossler system, Bessel collocation method, approximate solution, Nonlinear differential equation systems, Bessel functions of first kind Collocation points,

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