On the Computation of the Lagrange Multiplier for the Variational Iteration Method (VIM) for Solving Differential Equations

Main Article Content

N. Okiotor
F. Ogunfiditimi
M. O. Durojaye


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.

Integrating factor, operator D method, variational iteration method.

Article Details

How to Cite
Okiotor, N., Ogunfiditimi, F., & Durojaye, M. O. (2020). On the Computation of the Lagrange Multiplier for the Variational Iteration Method (VIM) for Solving Differential Equations. Journal of Advances in Mathematics and Computer Science, 35(3), 74-92,. https://doi.org/10.9734/jamcs/2020/v35i330261
Original Research Article


He JH. Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics. Int. Journal. Turbo Jet Eng. 1997;14(1):23-28.

Mehmood A, Awan FJ, Mohyud-Din ST. Comparison of Lagrange multiplier for nonlinear BVPs. International Journal of Modern Mathematical Science. 2003;5(3):156-165.

Wu G. Challenge in the variational iteration method- A new approach to identification of the Lagrange multipliers. Journal of King Daud University-Science. 2013;25:175-178.

He JH, Wu X. Variational iteration method: New development and application. Comp. Math. Applications. 2007;54:881-894.

Wu G, Baleanu D. Variational iterartion method for fractional calculus- a universal approach by Laplace transform. Advances in Differential Equation a Springer Open Journal. 2013;18.

Altina D, Ugor O. Generalization of the Lagrange multipliers for variational iteration applied to systems of differential equations. Mathematical and Computer Modelling. 2011;54:2040-2050.

Abbasbandy S. A new application of He’s variational iteration method for quadratic riccati differential equation by using adomian’s polynomials. Journal of Computational and Applied Mathematics. 2007;207:59-63.

Mohyud-Din ST, Noor MN, Noor KI. Variational iteration method for Burgers’ and coupled Burgers’ equations using He’s polynomials. Zeitschrift fur Naturforschung A. 2010;65:265-267.

Wazwaz A. Linear and non linear differential equations, methods and applications. Higher Edu. Press, Beijin/Springer-Verley Heidelberg; 2011.

Wazwaz A. The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients. Cent. Eur. J. Eng. 2014;4(1):64-71.

Dass HK. Advance engineering mathematics for the students of M.E, D.E and other engineering examination. Chands & Company Ltd, Ram Nagar, New delhi-110055; 2008.

Tseng ZS. Higher order linear equations with constant coefficients; 2014.


Rabie ME, Elzaki TM. A study of some systems of nonlinear partial differential equations by using adomian and modified decomposition methods. African Journal of Mathematics and Computer Science Research; 2014.

Wazwaz A. Variational iteration method for solving linear and nonlinear systems of PDE’s. Computer and Mathematics with Applications. 2007;54:895-902.