International Journal of Research and Scientific Innovation (IJRSI)
Numerical Solution of Heat Equation by Variational Iteration Method
Published October 23, 2025 • Vol. 12, Issue 9, pp. 4591–4596Open Access
DOI: 10.51244/IJRSI.2025.120800416
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.
Keywords: Heat equation, numerical solution, variational iteration method, Lagrange multiplier
| Journal | International Journal of Research and Scientific Innovation (IJRSI) |
|---|---|
| ISSN | 2321-2705 |
| Volume / Issue | Volume 12, Issue 9 |
| Pages | 4591–4596 |
| Publication date | October 23, 2025 |
| DOI | 10.51244/IJRSI.2025.120800416 |
| Publisher | RSIS International |
| License | Open Access |
How to cite this article
Haziem M. Hazaimeh (2025). Numerical Solution of Heat Equation by Variational Iteration Method. International Journal of Research and Scientific Innovation (IJRSI), 12(9), 4591-4596. https://doi.org/10.51244/IJRSI.2025.120800416
BibTeX
@article{Haziem2025,
title = {Numerical Solution of Heat Equation by Variational Iteration Method},
author = {Haziem M. Hazaimeh},
journal = {International Journal of Research and Scientific Innovation (IJRSI)},
volume = {12},
number = {9},
pages = {4591--4596},
year = {2025},
doi = {10.51244/IJRSI.2025.120800416},
publisher = {RSIS International}
}