Variational Iteration Decomposition method for Numerical Solution of Boundary Value Problems with Mamadu-Njoseph Polynomials

Abstract

In this paper, we seek the numerical solution of boundary value problems through an elegant mixture of the variational iteration method (VIM) and Adomian decomposition method (ADM) called the Variational iteration decomposition method (VIDM). In VIDM, the correction functional is first constructed and the general Lagrange multiplier is calculated. The initial approximation is uniquely determined by employing Mamadu-Njoseh polynomials as ansatz (test) functions satisfying the prescribed condition at the lower boundary x=a at in the interval [a,b]. In the nonlinear problems, the nonlinear terms are substituted with Adomian polynomials. The method is applied to selected linear and nonlinear boundary value problems of fifth order and the results obtained show that the method converges rapidly to the exact solution with few iterations. Results obtained are presented in graphs and in tables. Maple 18 software was used in executing all computational frameworks.