What is "chebfun"

Chebfun is a free/open-source software system written in MATLAB for numerical computation with functions of a real variable. It is based on the idea of overloading MATLAB's commands for vectors and matrices to analogous commands for functions and operators. Thus, for example, whereas the SUM command in MATLAB adds up the elements of a vector, the SUM command in Chebfun evaluates a definite integral. Similarly the backslash command in MATLAB becomes a Chebfun command for solving differential equations.

The mathematical basis of Chebfun is numerical algorithms involving piecewise polynomial interpolants and Chebyshev polynomials, and this is where the name "Cheb" comes from. The package aims to combine the feel of symbolic computing systems like Maple and Mathematica with the speed of floating-point numerics.

The Chebfun project is based in the Mathematical Institute at the University of Oxford and was initiated in 2002 by Lloyd N. Trefethen and his student Zachary Battles. The most recent version, Version 5.3.0, was released on November 26, 2015.

On the 4th of March 2013, Chebfun2, a software system that extends Chebfun to two dimensions, was made publicly available.