Lucas Polynomial Approach for Second Order Nonlinear Differential Equations

Abstract

This paper presents the Lucas polynomial solution of second-order nonlinearordinary differential equations with mixed conditions. Lucas matrix method is based oncollocation points together with truncated Lucas series. The main advantage of the methodis that it has a simple structure to deal with the nonlinear algebraic system obtained frommatrix relations. The method is applied to four problems. In the first two problems, exactsolutions are obtained. The last two problems, Bratu and Duffing equations are solvednumerically; the results are compared with the exact solutions and some other numericalsolutions. It is observed that the application of the method results in either the exact oraccurate numerical solutions.