Transformation of Parabolic Partial Differential Equations into Heat Equation Using Hopf Cole Transform

Onuoha N. O.

Abstract: This paper is concerned with the transformation of four parabolic partial differential equations to heat equations using Hopf Cole transform. The transformation shows that Hopf Cole transform is a good mathematical transformation tool that can be applied to any parabolic partial differential equation that needs to be transformed to heat equation to obtain the solution.

Keywords: Hopf Cole transform, Parabolic partial differential equations, Black-Scholes equation, Variable coefficient partial differential equation, Constant coefficient partial differential equation