# Investigation of Finite Difference
Methods for Solving Partial Differential Equations

## Raymond Li

### Math 345: Advanced Mathematics Project

### Spring 2012

### Introduction

The application of partial differential equations in mathematical medicine
was the primary topic within this project. Specifically, investigating
the accuracy and efficiency of finite difference methods in solving
simple, 1-dimensional drug diffusion problems. The algorithms constructed
were then appropriated to a two-region model, whereby the delivery
vehicle is in contact with another surface (e.g. skin) and administering
the drug via diffusion. Furthermore, boundary conditions analysis is heavily
emphasized as finite difference formulations are dependent on both the
category of the partial differential equation and the type of
boundary conditions (i.e. Dirichlet, Neumann or Robin).

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Page Created: 6th December 2012.

Last Updated: 6th December 2012.