Generalization of the Expansion of the Lagrange Multiplier Identifier Integrals for the Variational Iteration Method

Abstract

This study presents a theorem for resolving certain integrals. These integrals usually arise in the Correction Functional of the Variational Iteration Method (VIM). Resolving these integrals in the Correction Functional of VIM enables the accurate determination of the Lagrange multiplier for the method, which in turn leads to faster convergence rate for the solution of VIM. The study begins with a brief overview of the Lagrange Multiplier and VIM. This is followed by the theorem and a few experimental problems considered to demonstrate the usefulness of the theorem in the implementation of VIM. Comparison of results obtained shows that accurately determined Lagrange Multiplier for VIM improves the convergence rate of the method compared to using approximately determined Lagrange multiplier for the scheme.  Evaluations are carried out using Maple 18 software.