  We use the nonstandard Fourier transform method, along with an established
nonstandard approach to ODE's, to find a solution to the heat equation, on
$(0,\infty)\times\mathcal{R}$, with a given boundary condition $g$ at $t=0$. We
use this result to find an algorithm, converging to a solution of this
equation, with applications to derivatives pricing in finance.
