Abstract: The heat equation is a fundamental partial differential equation (PDE) in mathematical physics, widely used to model the diffusion of heat in each medium over time. It arises in diverse fields such as engineering, physics, and even financial mathematics (where it models option pricing under the Black-Scholes framework). Solving the heat equation efficiently and accurately is a central problem in applied mathematics, and numerous methods have been developed to tackle it. Among these, two prominent approaches stand out: the Finite Difference Method (FDM) and the Finite Element Method (FEM). This article provides an in-depth comparison of these two methods, exploring their theoretical foundations, computational implementations, advantages, limitations, and practical applications. By the end, readers will have a clear understanding of how these methods differ and when each might be preferable.
Keywords: mathematical physics, financial mathematics, Finite Element Method (FEM).
Title: A Comprehensive Comparison of Two Methods for Solving the Heat Equation
Author: Ahmad M. D. Al-Eybani
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
Vol. 13, Issue 1, April 2025 - September 2025
Page No: 3-7
Research Publish Journals
Website: www.researchpublish.com
Published Date: 09-April-2025
