Investigation of Finite Difference Methods for Solving Partial Differential Equations

Raymond Li

Math 345: Advanced Mathematics Project

Spring 2012


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.