Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden Type

Abstract

The aim of this study is present an effective and correct technique for solving differential equations of Lane-Emden type as initial value problems. In this work, a numerical method named as the Fibonacci polynomial approximation method, for the approximate solution of differential equations of Lane-Emden type in term of Fibonacci polynomials are studied. A matrix equation can be solved depending on the matrix relations of Fibonacci polynomials and their derivatives, and their reduced form to the solution of differential equations of Lane-Emden type, characterized by a system of algebraic equations with the unknown Fibonacci coefficients. Also, numerical results with comparisons are given to confirm the reliability of the proposed method for differential equations of Lane-Emden type.