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

Abstract

The aim of this study is to provide an effective and accurate technique for solving differential equations of Lane-Emden type as initial value problems. In this study, a numerical method called Fibonacci polynomial approximation method (FPAM) establish for approximate solution of Lane-Emden type differential equations by using Fibonacci polynomials. A matrix equation can be solved depending on the reduced form of the Lane-Emden type differential equations, which is characterized by an algebraic equation system, with the matrix relations of Fibonacci polynomials and their derivatives and their unknown Fibonacci coefficients. In addition, numerical results are given by comparisons to confirm the reliability of the proposed method for Lane-Emden type differential equations.

Fibonacci polynomials for the numerical solution of variable‐order space‐time fractional Burgers‐Huxley equation

“…Due to the advantages of the FPs which have a very simple structure (built through the recursive Fibonacci relation), the FPs have been widely studied and regarded as an important class of polynomials to provide the accurate approximations of mathematical systems. Çakmak 15 adapted the FPs for solving Lane-Emden type equations. These polynomials are used in Mirzaee and Hoseini 16 to solve systems of integro-differential equations.…”