What is Chebfun?
Chebfun is an open-source software system for numerical computing with functions. The mathematical basis of Chebfun is piecewise polynomial interpolation implemented with what we call “Chebyshev technology”. The foundations are described, with Chebfun examples, in Approximation Theory and Approximation Practice. Chebfun has extensive capabilities for dealing with linear and nonlinear differential and integral operators, and it also includes continuous analogues of linear algebra notions like QR and singular value decomposition. The Chebfun2 extension works with functions of two variables defined on a rectangle in the $x$-$y$ plane. To get a sense of the breadth and power of Chebfun, a great place to start is by looking at our Examples.
Chebfun was invented in 2002 as part of Zachary Battles' DPhil thesis and has grown into a large open-source project hosted on GitHub.