New technique for solving Lane-Emden equation with Vieta-Fibonacci polynomials

الملخص EN

In the present work, new efficient iterative algorithm is presented for solving Lane-Emden equation with initial conditions.

The solution is considered as a linear combination of Vieta-Fibonacci polynomials with unknown coefficients.

First, the Vieta-Fibonacci polynomials are presented with some new important properties.

A new exact formula for finding operation matrix of derivative for the Vieta-Fibonacci polynomials is constructed.

Using such new properties the original Lane-Emden equation is transformed to the solution of algebraic equation with small-unknown coefficients.

The obtained solution is in the form of a power series with easily computable coefficients.

Comparison with some known exact and approximate solutions shows that the proposed solution is highly accurate.