Dual solutions for nonlinear boundary value problems by the variational iteration method

Abstract

Purpose

The purpose of this paper is to use the variational iteration method (VIM) for studying boundary value problems (BVPs) characterized with dual solutions.

Design/methodology/approach

The VIM proved to be practical for solving linear and nonlinear problems arising in scientific and engineering applications. In this work, the aim is to use the VIM for a reliable treatment of nonlinear boundary value problems characterized with dual solutions.

Findings

The VIM is shown to solve nonlinear BVPs, either linear or nonlinear. It is shown that the VIM solves these models without requiring restrictive assumptions and in a straightforward manner. The conclusions are justified by investigating many scientific models.

Research limitations/implications

The VIM provides convergent series solutions for linear and nonlinear equations in the same manner.

Practical implications

The VIM is practical and shows more power compared to existing techniques.

Social implications

The VIM handles linear and nonlinear models in the same manner.

Originality/value

This work highlights a reliable technique for solving nonlinear BVPs that possess dual solutions. This paper has shown the power of the VIM for handling BVPs.

Citation

Wazwaz, A.-M. (2017), "Dual solutions for nonlinear boundary value problems by the variational iteration method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 1, pp. 210-220. https://doi.org/10.1108/HFF-10-2015-0442