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Research Article Open access CC BY 4.0

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

N. Okiotor, F. Ogunfiditimi, M. O. Durojaye

Journal of Advances in Mathematics and Computer Science · pp. 74–92 · Published 10 Jun 2020

10.9734/jamcs/2020/v35i330261

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.

Integrating factor operator D method variational iteration method.

References (12)

  1. 1 Variational iteration method—Some recent results and new interpretations [DOI]
  2. 2 Variational iteration method: New development and applications [DOI]
  3. 3 New applications of variational iteration method [DOI]
  4. 4 Semi-Inverse Method of Establishing Generalized Variational Principles for Fluid Mechanics With Emphasis on Turbomachinery Aerodynamics [DOI]
  5. 5 A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials [DOI]
  6. 6 Variational iteration method for fractional calculus - a universal approach by Laplace transform [DOI]
  7. 7 The variational iteration method for rational solutions for KdV, K (2,2), Burgers, and cubic Boussinesq equations [DOI]
  8. 8 The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients [DOI]
  9. 9 Challenge in the variational iteration method – A new approach to identification of the Lagrange multipliers [DOI]
  10. 10 Variational iteration method for solving cubic nonlinear Schrödinger equation [DOI]
  11. 11 A study of some systems of nonlinear partial differential equations by using Adomian and modified decomposition methods [DOI]
  12. 12 Variational Iteration Method for Burgers’ and Coupled Burgers’ Equations Using He’s Polynomials [DOI]

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