Reducing Parabolic Partial Differential Equations to Canonical Form

Reducing Parabolic Partial Differential Equations to Canonical Form

Eur.J.App.Maths 5, 159-164, 1994

A simple method of reducing a parabolic partial differential equation to canonical form if it has only one term involving second derivatives is the following: find the general solution of the first-order equation obtained by ignoring that term and then seek a solution of the original equation which is a function of one more independent variable. Special cases of the method have been given before, but are not well known.

Applications occur in fluid mechanics and the theory of finance, where the Black-Scholes equation yields to the method, and where the variable corresponding to time appears to run backwards, but there is an information-theoretic reason why it should.

PDF version 96K

School of Engineering and Computer Science
School of Mathematics, Statistics and Operations Research
 
Contact MSCS | Section Map | Glossary | A-Z of Victoria University Sites | Disclaimer | RSS feed RSS FeedBack to top ^

Page Updated: 26 Apr 2006. © Victoria University of Wellington, New Zealand, unless otherwise stated