Study of Numerical Methods for Heat Equation in 1-D

Abstract

This thesis presents a comprehensive exploration of the one-dimensional heat equation, a fundamental model in understanding heat distribution within materials. Tracing its historical roots to the pioneering works of Joseph Fourier and other eminent scientists in the 19th century, this equation stands as a cornerstone in mathematical physics, offering insights into heat transfer phenomena along a single spatial dimension. The research delves into the theoretical foundations, historical evolution, and practical applications of the equation, encompassing analytical solutions, numerical methods, and their relevance in diverse fields such as physics, engineering, and materials science. By scrutinizing the equation's mathematical intricacies and leveraging modern computational techniques, this study aims to unravel its complexities and harness its predictive power. Ultimately, this investigation contributes to a deeper understanding of heat transfer dynamics and underscores the equation's pivotal role in shaping scientific inquiry and technological advancements.