A Legendre-homotopy method for the solutions of higher order boundary value problems

Abstract

In this paper, the Legendre-homotopy analysis method is proposed using orthogonal Legendre polynomials for the approximate solutions of linear and nonlinear higher order boundary value problems. The deformation equations obtained in this case are easily integrable and the calculations involved in the algorithm are much simpler than the standard homotopy analysis method. The method is numerically illustrated by application on linear and nonlinear higher order boundary value problems. The absolute errors in the approximate solution values are calculated and compared with the results available in literature. The approximate solutions are also compared with the exact solutions through graphical illustrations. The numerical and graphical comparisons reveal that the presented method gives highly accurate results.