Diffusion Problems

Abstract

To begin the study of finding numerical solutions of partial differential equations we begin with diffusion problems. In physical terms these are problems that involve motion or transport of particles (ions, molecules, etc.) from areas of higher concentration to areas of lower concentration. Simple examples are the spread of a drop of ink dropped into water and the melting of an ice cube. Diffusion is also a key component in the formation of dendrites when liquid metal cools, as well as in the chemical signals responsible for pattern formation (Figure 3.1). Other interesting applications of diffusion arise in the study of financial assets as expressed by the Black-Scholes theory for options pricing and in the spread of infectious diseases ([2002], [2001]).