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 , with a given boundary condition at . 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}
}