Comparative solutions to fifth order boundary value problems using variation iteration decomposition method and variation iterational method with Chebychev polynomials

Abstract

In this paper, we compare solutions from variation iteration decomposition method (VIDM) and variationiteration method (VIM) for the numerical treatment of fifth order boundary value problems using Chebychev polynomials as trial functions. The Chebychev polynomials are employed as trial functions in seeking the initial approximation at the lower boundary condition. The unknown parameters are computed at the upper boundary at each iteration. It is evident from the numerical evidences that VIM converges faster and better compared to VIDM. However, both iterative schemes are straightforward, explicit and adequate requiring no hidden or weak assumptions. Maple 18 software was used to execute all computations throughout this paper.