Just wanted to say that ApproxFun looks incredibly cool. I've been following the development of Chebfun (http://www2.maths.ox.ac.uk/chebfun/) in matlab for a few years, and it's really beautiful work. It helps that Trefethen is such a great expository writer. Julia seems like a significantly better environment than matlab is for implementing these ideas.
For anyone looking to get a high level overview of the topic I'd recommend starting with "Computing Numerically With Functions Instead Of Numbers": http://www2.maths.ox.ac.uk/chebfun/publications/trefethen_functions.pdf On Sunday, March 23, 2014 6:04:25 PM UTC-7, Sheehan Olver wrote: > > > I tagged a new release for ApproxFun ( > https://github.com/dlfivefifty/ApproxFun) with major new features that > might interest people. Below are ODE solving and random number sampling > examples, find more in ApproxFun/examples. The code is meant as alpha > quality, so don't expect too much beyond the examples. There is > rudimentary support for PDE solving (e.g. Helmholtz in a square), but it's > reliability is limited without a better Lyapanov solver ( > https://github.com/JuliaLang/julia/issues/5814). > > Cheers, > > Sheehan > > > > > Pkg.add("ApproxFun") > using ApproxFun > > *ODE Solving: solve the Airy equation on [-1000,10]* > > x=Fun(identity,[-2000.,10.]) > d=x.domain > D=diff(d) > ai=[dirichlet(d),D^2 - x]\[airyai(-2000.),0.] > plot(ai) > > > > > *Random number sampling: Sample a 2D Cauchy distribution on (-∞,∞)^2* > > f = Fun2D((x,y)->1./(2π.*(x.^2 .+ y.^2 .+ 1).^(3/2)),Line(),Line()) > r = sample(f,100) > > >
