This is to announce a new version of ApproxFun (https://github.com/dlfivefifty/ApproxFun.jl), a package for approximating functions. The biggest new feature is support for PDE solving. The following lines solve Helmholtz equation u_xx + u_yy + 100 u = 0 with the solution held to be one on the boundary:
d=Interval()⊗Interval() # the domain to solve is a rectangle u=[dirichlet(d),lap(d)+100I]\ones(4) # first 4 entries are boundary conditions, further entries are assumed zero contour(u) # contour plot of the solution, requires GadFly PDE solving is based on a recent preprint with Alex Townsend (http://arxiv.org/abs/1409.2789). Only splitting rank 2 PDEs are implemented at the moment. Examples included are: "examples/RectPDE Examples.ipynb": Poisson equation, Wave equation, linear KdV, semiclassical Schrodinger equation with a potential, and convection/convection-diffusion equations. "examples/Wave and Klein–Gordon equation on a square.ipynb": On-the-fly 3D simulation of time-evolution PDEs on a square. Requires GLPlot.jl (https://github.com/SimonDanisch/GLPlot.jl). "examples/Manipulate Helmholtz.upynb": On-the-fly variation of Helmholtz frequency. Requires Interact.jl (https://github.com/JuliaLang/Interact.jl) Another new feature is faster root finding, thanks to Alex.
