The Function of Diffusion

Overview

Objectives/Goals The goal of my project was to design a computer program that could determine the rate of diffusion between solids using the Scheme programming language. Methods/Materials First I learned how to program using "How to Design Programs" and Dr. Scheme. Next I designed a program that computes first-order differential equations, and then I designed a program that computes second-order differential equations. Finally I started working on the diffusion equation. Results The two programs that were designed both returned their expected results. The constants in the second-order differential equation caused the results to change. Conclusions/Discussion The fact that different results were obtained from the second-order differential equation depending on the constants means that a different diffusion constant would change the rate of diffusion, and this should be researched further. Also, the Improved Euler method will be researched further, as it is a more accurate way of solving differential equations. Because the diffusion equation is just a complicated second-order equation, and I successfully wrote a program that solves a second-order differential equation, it can be assumed that the diffusion equation can be programmed.

Competition history

• CSEF 2003 Mathematics & Software · Entry J1202

Resources

• CSEF project summary ↗

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