A Residual Method Using Bézier Curves for Singular Nonlinear Equations of Lane-Emden Type

Meltem Adiyaman, Volkan Oger

Abstract


In this article, we introduce a new method to solve a singular non-linear equation of the Lane-Emden type by approximating the solution with Bernstein polynomials. This method is based on the minimization of a residual function using Taylor’s series expansion. We also apply this method to problems that are solved by other methods and the obtained results show that
our method is efficient, applicable and has great potential than others.


Keywords


Bézier curves; Bernstein polynomials; continuous linear approximation; Lane- Emden equations; singular nonlinear differential equations.

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