A study of variational iteration method for solving various types of problems

Downloads

Abstract

This paper presents the application of He’s Variational Iteration Method for various types of problems. This
method is applied to find successive approximate solutions of first order differential equation with single condition,
second order differential equations with two conditions, an isoperimetric problem and Volterra integral equations
of second kind. It was shown that they are converging to their exact solutions. The successive approximations
and exact solution are shown graphically.

Keywords:

Successive Approximate Solution, Variational Iteration Method

Mathematics Subject Classification:

Mathematics
  • E.Rama Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, Telangana State, India.
  • K.Somaiah Department of Mathematics, Kakatiya University, Vidyaranyapuri, Warangal, Telangana State, India.
  • K.Sambaiah Flat No.101, Riddhi’s Pebble, Madhapur, Hyderabad, Telangana State, India.
  • Pages: 701-708
  • Date Published: 01-01-2021
  • Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

J.H. He, A new approach to nonlinear partial differential equations, Comm.in Nonlinear Sci. and Numer. Simul.2 (4), 230-235, (1997).

J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comp. Methods Appl. Mech. Engg., Vol.167, 57-68, (1998).

J.H. He, Approximate solution of non linear differential equations with convolution product non-linearities, Comp. Methods Appl. Mech. Engg. , Vol.167,69-73, (1998).

Fateme Ghomanjani, Sara Gaderi, Varitional iterative method applied to variational problems with moving boundaries, Appl. Maths, 3, 395-402, (2012).

Junfeng Lu, Variational iteration method for solving two-point boundary value problems, $J$. of Comp. and Appl. Math, 207, 92-95, (2007).

Sallid Abbasbandy, Elyas Shivanian, Application of the variational iteration method for system of the non-linear Volterra's integro-differential equations, Math and Comp. Applications, vol. 14, No.2, 147-159, (2009).

Abdal-Majid waz waz, The variational iteration method for solving linear and non-linear ODEs and scientific models with variable coefficients, Cent. Euro. Jr. Engg. , $4(1), 64-71,(2014)$.

J.H.He Variational Iteration method a kind of non-linear analytical technique: some examples, Int. $J r$ of nonlinear Mechanics, Vol.34, 699-708, (1999).

Ji-Huan He,Xu-Hong Wu,Variational Iteration Method: New development and applications, Science Direct, Compu. and Mathematics Applications. ,54, 881-894, $(2007).

Metrics

Metrics Loading ...

Published

01-01-2021

How to Cite

E.Rama, K.Somaiah, and K.Sambaiah. “A Study of Variational Iteration Method for Solving Various Types of Problems”. Malaya Journal of Matematik, vol. 9, no. 01, Jan. 2021, pp. 701-8, https://www.malayajournal.org/index.php/mjm/article/view/1116.

Issue

Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

Section

Articles

License

Copyright (c) 2021 MJM

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.