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

Abstract

The aim of this study is presentan effective and correct technique for solving differential equations ofLane-Emden type as initial value problems. In this work, a numerical method namedas the Fibonacci polynomial approximation method, for the approximate solutionof differential equations of Lane-Emden type in term of Fibonacci polynomialsare studied. A matrix equation can be solved depending on the matrix relationsof Fibonacci polynomials and their derivatives, and their reduced form to thesolution of differential equations of Lane-Emden type, characterized by asystem of algebraic equations with the unknown Fibonacci coefficients. Also, numericalresults with comparisons are given to confirm the reliability of the proposed methodfor differential equations of Lane-Emden type.

Keywords

• diferansiyel fark denklemleri
• fibonacci polinomları
• lane-emden denklemi
• operasyonel matris
• polinom yaklaşımı
• differential- difference equations
• fibonacci polynomials
• lane-emden equation
• operational matrix
• polynomial approach