This is really great idea Sheehan! I love the idea of Chebfun and extending it to Julia, specially aiming at a general and powerful PDE solver sounds really good. Certainly it will be very useful.
Thanks again!! On Wednesday, September 10, 2014 7:22:36 PM UTC-3, Sheehan Olver wrote: > > > 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. >
