Modified operational matrix method for second-order nonlinear ordinary differential equations with quadratic and cubic terms

Abstract

In this study, by means of the matrix relations between the Laguerre polynomials, and their derivatives, a novel matrix method based on collocation pointsis modified and developed for solving a class of second-order nonlinear ordinarydifferential equations having quadratic and cubic terms, via mixed conditions.The method reduces the solution of the nonlinear equation to the solution of amatrix equation corresponding to system of nonlinear algebraic equations withthe unknown Laguerre coefficients. Also, some illustrative examples along withan error analysis based on residual function are included to demonstrate thevalidity and applicability of the proposed method.