Chebfun is an open-source software system for numerical computing with functions. The mathematical basis is piecewise polynomial interpolation implemented with what we call “Chebyshev technology”. The foundations are described, with Chebfun examples, in the book Approximation Theory and Approximation Practice (L. N. Trefethen, SIAM 2013). Chebfun has extensive capabilities for dealing with linear and nonlinear differential and integral operators, and 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.
Most Chebfun commands are overloads of familiar MATLAB commands — for example sum(f) computes an integral, roots(f) finds zeros, and u = L\f solves a differential equation.
To get a sense of the breadth and power of Chebfun, a good place to start is by looking at our Examples (http://www.chebfun.org/examples/) or the introductory Guide (http://www.chebfun.org/docs/guide/).
Please contact us with any questions/comments at email@example.com.
Updated to v5.6.0
Chebfun v5.3.0 has been released. For details on what has changed, see the release notes at htttp://www.chebfun.org.
Updated October 29, 2015.