The use of He's variational iteration method for solving the one-dimensional parabolic equation with non-classical boundary conditions

Abstract

Over the last 15 years, the He’s variational iteration method (HVIM) has been applied to obtain formal solutions to a wide class of differential equations. This method leads to computable, efficient, solutions to linear and nonlinear operator equations. The parabolic partial differential equations with non-classical boundary conditions model various physical problems. The aim of this paper is to investigate the application of HVIM for solving the second-order linear parabolic partial differential equation with non-classical boundary conditions. The HVIM provides a reliable technique that requires less work when compared with the traditional techniques such as the Adomian decomposition method (ADM). The present approach can be used and extended for investigating more scientific applications.