Ordinary Differential Equations and Applied Dynamics Commons^™

Numerical Solutions Of Singular Nonlinear Ordinary Differential Equations Using Said-Ball Polynomials, Mobarek A. Assabaai, Ahmed Kherd

Emirates Journal for Engineering Research

In this article, the collocation method based on Said-Ball polynomials have been used to solve the singular nonlinear ordinary differential equations of various orders numerically. An operational matrix forms of these ordinary differential equations are obtained from Said-Ball polynomial with variated relations of solution and different derivatives. The presented method reduces the given problem to a system of nonlinear algebraic equations, which removed the singularity of ordinary differential equations. Resulting system is solved using Newton's iteration method to get the coefficients of Said-Ball polynomials. We obtained approximate solutions of the problem under study. Numerical results have been obtained and compared …