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.

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