On the approximation of particular solution of nonhomogeneous linear differential equation with Legendre series

Abstract

In this study, we propose an approximation method for particular solutions of the nonhomogeneous second-order differential equations by truncated Legendre series. Particulary, the govern problem is a linear differential equation with constant coefficients. The choice of series solutions depends upon the complementary solutions and the approximate nonhomogeneous terms. An upper bound for the approximation error is formulated. Some examples are presented to demonstrate the validity of the proposed method.