Explicit Scheme
In one dimension we have the following equation
\begin{equation*}
\nabla^2 u(x,t) =\frac{\partial u(x,t)}{\partial t},
\end{equation*}
or
\begin{equation*}
u_{xx} = u_t,
\end{equation*}
with initial conditions, i.e., the conditions at
t=0 ,
\begin{equation*}
u(x,0)= g(x) \hspace{0.5cm} 0 < x < L
\end{equation*}
with
L=1 the length of the
x -region of interest.