This paper presents a numerical method that solves heat equations using He's variational iteration method (HVIM). It showed that the solutions obtained from the developed method converged rapidly to the exact solutions within three iterations. It is also found that HVIM gives very trivial solutions for the nonlinear differential equations with zero initial condition.
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.
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