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

Abstract

PurposeThe purpose of this paper is to use the variational iteration method (VIM) for studying boundary value problems (BVPs) characterized with dual solutions.Design/methodology/approachThe 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.FindingsThe 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/implicationsThe VIM provides convergent series solutions for linear and nonlinear equations in the same manner.Practical implicationsThe VIM is practical and shows more power compared to existing techniques.Social implicationsThe VIM handles linear and nonlinear models in the same manner.Originality/valueThis 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.