Open AccessA collocation method based on Genocchi operational matrix for solving Emden-Fowler equations
Author(s) -
Abdulnasir Isah,
Chang Phang
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1489/1/012022
Subject(s) - mathematics , collocation (remote sensing) , algebraic equation , matrix (chemical analysis) , orthogonal collocation , differential equation , collocation method , mathematical analysis , algebra over a field , ordinary differential equation , pure mathematics , computer science , nonlinear system , physics , materials science , quantum mechanics , machine learning , composite material
In this paper, we solved the first kind and second kind Emden-Fowler type equations by using scheme involving Genocchi polynomials. Using the nice properties of Genocchi polynomials, which is the member of Appell polynomials, we construct the Genocchi operational matrices of derivative. Then, we use collocation scheme together with this operational matrix to transform the Emden-Fowler equation to a matrix equation. Hence we obtain a system of algebraic equations with unknown coefficients, solving this system will lead to the solution of Emden-Fowler type equations. This Emden-Fowler equation is a singular second order differential equation which many numerical methods may fail to solve the problem effectively. Error analysis on standard Emden-Fowler type equations for this proposed method is shown. We finally solve some numerical examples and compare to other numerical scheme to show the efficiency, simplicity and accuracy of the method.