TY - JOUR
T1 - Simplifying the variational iteration method
T2 - A new approach to obtain the Lagrange multiplier
AU - Tomar, Saurabh
AU - Singh, Mehakpreet
AU - Vajravelu, Kuppalapalle
AU - Ramos, Higinio
N1 - Publisher Copyright:
© 2022 International Association for Mathematics and Computers in Simulation (IMACS)
PY - 2023/2
Y1 - 2023/2
N2 - The variational iteration method (VIM) has been in the last two decades, one of the most used semi-analytical techniques for approximating nonlinear differential equations. The notion of VIM is based on the identification of the Lagrange multiplier using the variational theory. The performance of the method is highly dependent on how the Lagrange multiplier is determined. In this paper, a novel method for calculating the Lagrange multiplier is provided, making the VIM more efficient in solving a variety of nonlinear problems. To illustrate the effectiveness of the new approach, a standard nonlinear oscillator problem is tested and the results demonstrate that only one iteration leads to an excellent outcome.
AB - The variational iteration method (VIM) has been in the last two decades, one of the most used semi-analytical techniques for approximating nonlinear differential equations. The notion of VIM is based on the identification of the Lagrange multiplier using the variational theory. The performance of the method is highly dependent on how the Lagrange multiplier is determined. In this paper, a novel method for calculating the Lagrange multiplier is provided, making the VIM more efficient in solving a variety of nonlinear problems. To illustrate the effectiveness of the new approach, a standard nonlinear oscillator problem is tested and the results demonstrate that only one iteration leads to an excellent outcome.
KW - Lagrange multiplier
KW - Nonlinear oscillator
KW - Variational iteration method
KW - Variational principle
UR - http://www.scopus.com/inward/record.url?scp=85138995778&partnerID=8YFLogxK
U2 - 10.1016/j.matcom.2022.09.003
DO - 10.1016/j.matcom.2022.09.003
M3 - Article
AN - SCOPUS:85138995778
SN - 0378-4754
VL - 204
SP - 640
EP - 644
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -