Editing Heat equation (section)

=== Financial Mathematics ===

The heat equation arises in a [[List of natural phenomena|number of phenomena]] and is often used in [[financial mathematics]] in the [[Mathematical model|modeling]] of [[Option (finance)|options]]. The [[Black–Scholes]] option pricing model's [[differential equation]] can be transformed into the heat equation allowing relatively easy solutions from a familiar body of mathematics. Many of the extensions to the simple option models do not have closed form solutions and thus must be solved numerically to obtain a modeled option price. The equation describing pressure diffusion in a porous medium is identical in form with the heat equation. [[Diffusion]] problems dealing with [[Dirichlet boundary conditions|Dirichlet]], [[Neumann boundary conditions|Neumann]] and [[Robin boundary condition]]s have closed form analytic solutions {{harv|Thambynayagam|2011}}.