Discrete Dynamics in Nature and Society 
Volume 6 (2001), Issue 3, Pages 157-169
doi:10.1155/S1026022601000176

Comparing algebraic and numerical solutions of classical diffusion process equations in computational financial mathematics

Andreas Ruffing,1,2 Patrick Windpassinger,2 and Stefan Panig2

 1Center for APPlied Mathematics and Theoretical Physics, University of Maribor, Krekova Ulica 2, Maribor SLO-2000, Slovenia
2Zentrum Mathematik, Technische Universität München, Arcisstrasse 21, München D-80333, Germany
Received 28 August 2000

Abstract

We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics.