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.
News:
New version available (March 2012): Chebfun V4.2.2194. Release notes available here.
April '12: Oxford Postdoctoral position in algorithms and mathematics related to Chebfun. Details.
Events:
"Chebfun and Beyond" workshop in Oxford, September 17-19, 2012. Details here.
(Speakers include Leslie Greengard, Nick Higham, Cleve Moler, and Nick Trefethen).
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)
Stefan Güttel, 18th April 2012
Mohsin Javed, 17th April 2012
Nick Trefethen, 10th April 2012
