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

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.