An analytic study on the Euler-Lagrange equation arising in calculus of variations

Abstract

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. Several illustrative examples are given to demonstrate the effectiveness of the present method.