Solves an ODE with boundary values using a Bezier cure.

This was my submission for end year project in AM3611 at the University of Western Ontario. Topics were chosen by students based on interest, with aid being given by the professor where necessary when picking a topic.

I originally heard about Bézier curves while taking this course, and was looking for a end year project idea. I wanted to explore them a bit more, but was unsure how.

Later, I learned about the collocation method in my numerical analysis course, I had an instant light bulb and wondered if a Bézier curve could be used as the basis function in the collocation method (Bézier curves are also called Bernstein polynomials), so I tried it! The margin of error is LARGE. Well, small in some contexts, but large in this one

A collocation method can be used to solve a boundary volue problem using a Bézier curve. This is an exploration of that method.

This ODE solver does not solve many ODE's, and when it does, it isn't very accurate. But that wasn't the point of me coming up with this project. The point of the project was to explore ways of solving a BVP (boundary value problem) that were original, while learning more about scientific programming in C++.

Maybe a future project could be a real ODE solver with a GUI to make up for this bamboozle.