Welcome to Chebfun! Numerical Computing with Functions
Chebfun is a collection of algorithms and an open-source software system in object-oriented MATLAB which extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. It also implements continuous analogues of linear algebra notions like the QR decomposition and the SVD, and solves ordinary differential equations. The mathematical basis of the system combines tools of Chebyshev expansions, fast Fourier transform, barycentric interpolation, recursive zerofinding, and automatic differentiation. The project was initiated by Nick Trefethen and Zachary Battles in 2002, and the differential equations side of Chebfun was created by Toby Driscoll of the University of Delaware beginning in 2008. The project is directed by Nick Hale.
News:
New version available (Sept 2011): Chebfun V4.1.1864. Release notes available here.
Feb '12: Oxford PhD studentship in algorithms and mathematics related to Chebfun. Details here.
Three quick examples: (For more, see Chebfun Examples and the Chebfun Guide)
>> x = chebfun('x',[0 10]); sum(sin(sin(x)))
ans = 1.629603118459496
What's the maximum of sin(x)+sin(x2) over the same interval?
>> max(sin(x)+sin(x.^2))
ans = 1.985446580874100
What's the solution to u"-xu=1 with zero boundary conditions on [-20,20]?
>> L = chebop(@(x,u)diff(u,2)-x.*u,[-20,20],'dirichlet'); plot(L\1)
New Examples: (more available here)
Nick Trefethen, 25th January 2012
Asgeir Birkisson, 25th January 2012
Binh K. Lieu and Mihailo R. Jovanovic, 6th January 2012
