On The Analytical and Numerical Solutions of Heat Equation

Abstract

In this paper, we give first the general meaning and importance of partial differential equations, with stating some known types of the second-order linear partial differential. Furthermore, we show the classification to the associated types of initial-boundary conditions. Next, we will use separation of variables method to find a formula for the analytical solution of the heat equation in one-dimensional space. Finally, we compute the numerical solution of an initial-boundary problem of the heat equation in one-dimensional space, using Euler Explicit and Implicit finite different methods.