Numerical Solution of Heat Equation by Variational Iteration Method

Abstract

In this article, we study the one-dimensional heat equation, which models the diffusion of heat through a medium over time. To solve this equation numerically, we employ He’s Variational Iteration Method (VIM), a semi-analytical technique particularly effective for problems where exact solutions are intractable. The VIM relies on a correction functional that iteratively minimizes the equation’s residuals using a Lagrange multiplier. By repeating this process until convergence is achieved, we obtain an approximate solution to the heat equation.