Computer Science is the study of how computers work and how we can use them to solve problems. By studying computer science, we can use technology to make our lives easier and more efficient.

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.

Can a computer program calculate how fast atoms spread through a solid? Diffusion (the slow movement of particles from crowded areas to empty ones) is described by a second-order differential equation. Solving that equation by hand is slow and difficult.

You write programs in the Scheme language that solve first-order and then second-order differential equations. Both programs return their expected results. Changing the constants in the equation changes the rate of diffusion.

Because the diffusion equation is a type of second-order equation, a working solver for that type can be extended to model real diffusion between solids.

Title: The Function of Diffusion

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.

Summary Statement

My project is about programming the Diffusion Equation.

Help Received

Mr. Dan Anderson, my computer teacher, taught me programming skills and
beginning calculus.

Programming the Diffusion Equation

Designing a computer program to determine the rate of diffusion between solids

<h1><strong>1000 Science Fair Project Ideas by Subject</strong></h1><p>Looking for a science fair project idea? Each of our science fair project idea has complete instructions with video. Get ideas for your science projects, find extra resources for your class' scientific projects, or try a fun experiment at home! It doesn't matter what grade you're in, there's something for everyone!</p><p>You can find your perfect science fair project from the different science subjects below or from our <a href="https://www.all-science-fair-projects.com/category0.html#bottom">science fair project idea lists!</a></p>

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Math is all about numbers, patterns, and solving problems. Computer science is about using math and technology to create computer programs and solve real-world problems. Together, they help us understand how things work, how to solve problems, and how to use technology to make our lives better!

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Programming the Diffusion Equation

Hypothesis

Method & Materials

Results

Why do this project?

Also Consider

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