Exact Solutions for Some Singular Linear Ordinary Differential Equations of High Orders via NB1 Polynomials
Mobarek A. Assabaai *
Department of Mathematics, Hadhramout University, Mukalla, Yemen.
Ahmed Kherd
Department of Mathematics, Faculty of Computer Science and Engineering, Al-Ahgaff University, Mukalla, Yemen.
*Author to whom correspondence should be addressed.
Abstract
In this study, we numerically solve the singular linear ordinary differential equations (SLODEs) of higher order using the collocation method based on the NB1 polynomial. An operational matrix form of the given ordinary differential equations (ODEs), the relations of various solutions and the derivatives are obtained from NB1 polynomials. The proposed method reduces the given problem to a linear algebraic equation system, which removes the singularity of ordinary differential equations. The inverse matrix method is used to solve the resulting system to obtain the coefficients of NB1 polynomials. The obtained exact solutions to different problems of high orders show the reliability and accuracy of the presented method.
Keywords: Collocation method, NB1 polynomial, operational matrix form, singular differential equations