On the convergence of the variational iteration method

Authors

  • Ernest Scheiber retired, Romania

DOI:

https://doi.org/10.33993/jnaat451-1053

Keywords:

variational iteration method, ordinary differential equations, initial value problem
Abstract views: 379

Abstract

Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.

Downloads

Download data is not yet available.

References

T. Daly, Publishing Computational Mathematics, Notices of the AMS, 59 (2012) no. 2, pp. 320–321, http://dx.doi.org/10.1090/noti797 DOI: https://doi.org/10.1090/noti797

M. Inokuti, H. Sekine, T. Mura, General use of the Lagrange multiplier in Nonlinear Mathematical Physics, In Variational Methods in Mechanics and Solids, ed. Nemat-Nasser S., Pergamon Press, pp. 156-162, 1980, http://dx.doi.org/10.1016/B978-0-08-024728-1.50027-6 DOI: https://doi.org/10.1016/B978-0-08-024728-1.50027-6

J.H. He, Variational iteration method - Some recent results and new interpretations, J. Comput. Appl. Math.,207 (2007), pp. 3-17, http://dx.doi.org/10.1016/j.cam.2006.07.009 DOI: https://doi.org/10.1016/j.cam.2006.07.009

Z.M. Odibat, A study on the convergence of variational iteration method, Math. Computer Modelling, 51 (2010), pp. 1181-1192, http://dx.doi.org/10.1016/j.mcm.2009.12.034 DOI: https://doi.org/10.1016/j.mcm.2009.12.034

D. K. Salkuyeh, Convergence of the variational iteration method for solving linear systems of ODE with constant coefficients, Comp. Math. Appl.,56 (2008), pp. 2027-2033, http://dx.doi.org/10.1016/j.camwa.2008.03.030 DOI: https://doi.org/10.1016/j.camwa.2008.03.030

D. K. Salkuyeh, A. Tavakoli, Interpolated variational iteration method for initial value problems, arXiv:1507.01306v1, 2015, http://dx.doi.org/10.1016/j.apm.2015.10.037 DOI: https://doi.org/10.1016/j.apm.2015.10.037

E. Scheiber, From the numerical solution to the symbolic form, Bull. Transilvania University of Bra ̧sov, Series III, Mathematics, Informatics, Physics, 8(57) (2015) no. 1,

pp. 129–137.

M. Tatari, M. Dehghan, On the convergence of He’s variational iteration method. J. Comput. Appl. Math., 207 (2007), pp. 121-128, http://dx.doi.org/10.1016/j.cam.2006.07.017 DOI: https://doi.org/10.1016/j.cam.2006.07.017

M. Torvattanabun, S. Koonprasert, Convergence of the variational iteration method for solving a first-order linear system of PDEs with constant coefficients, Thai J. of Mathematics, Special Issue, pp. 1-13, 2009.

* * *, www.nutonian.com,

* * *, www.scilab.org

Downloads

Published

2016-09-19

How to Cite

Scheiber, E. (2016). On the convergence of the variational iteration method. J. Numer. Anal. Approx. Theory, 45(1), 87–96. https://doi.org/10.33993/jnaat451-1053

Issue

Section

Articles