Solving the Heat Equation using Nonstandard Analysis

2014/04/14 by de Piro, Tristram
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.3778

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,∞)\timesR, 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.

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