Solving the Heat Equation using Nonstandard Analysis
  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. 
Tristram de Piro
math.AP