On the Computation of the Lagrange Multiplier for the Variational Iteration Method (VIM) for Solving Differential Equations
N. Okiotor *
Department of Mathematics, University of Abuja, Abuja, Nigeria.
F. Ogunfiditimi *
Department of Mathematics, University of Abuja, Abuja, Nigeria.
M. O. Durojaye
Department of Mathematics, University of Abuja, Abuja, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this study, the Variational Iteration Method (VIM) is applied in finding the solution of differential equations with emphasis laid on the choice of the Lagrange multiplier used while employing VIM. Building on existing methods and variational theories, the operator D-Method and integrating factor are employed in certain aspects in the determination of exact Lagrange multiplier for VIM. When results of the computed exact Lagrange multiplier were compared with results of approximate Lagrange multiplier, it was observed that the computed exact Lagrange multiplier reduced significantly the number of iterations required to get a good approximate result, and in some cases the result converged to the exact solution after a single iteration. Evaluations are carried out using MAPLE Software.
Keywords: Integrating factor, operator D method, variational iteration method.