Zeitschrift für Angewandte und Computermathematik

One Dimensional Heat Equation and its Solution by the Methods of Separation of Variables, Fourier Series and Fourier Transform

Abstract

Lencha Tamiru Abdisa

The aim of this paper was to study the one-dimensional heat equation and its solution. Firstly, a model of heat equation, which governs the temperature distribution in a body, was derived depending on some physical assumptions. Secondly, the formulae in which we able to obtain its solution were derived by using the Method of separation of variables along with the Fourier series and the method of Fourier transform. Then after, some real-life applications of the equations were discussed through examples. Finally, a numerical simulation of the raised examples was studied by using MATLAB program and the results concluded that the numerical simulations match the analytical solutions as expected.