English

Solving the Heat Equation using Nonstandard Analysis

Analysis of PDEs 2014-04-16 v1

Abstract

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,)×R(0,\infty)\times\mathcal{R}, with a given boundary condition gg at t=0t=0. We use this result to find an algorithm, converging to a solution of this equation, with applications to derivatives pricing in finance.

Keywords

Cite

@article{arxiv.1404.3778,
  title  = {Solving the Heat Equation using Nonstandard Analysis},
  author = {Tristram de Piro},
  journal= {arXiv preprint arXiv:1404.3778},
  year   = {2014}
}
R2 v1 2026-06-22T03:50:50.431Z