On what kind of domain?
> On 17 Sep 2015, at 12:07 pm, Luke Stagner <[email protected]> wrote: > > It's actually a 2D non-linear, elliptic PDE (psi is a function of R,Z). I'm > thinking about created a Julia library for fusion/plasma physics and the > ability to quickly calculate magnetic equilibrium would be a killer feature. > > > On Wednesday, September 16, 2015 at 6:46:09 PM UTC-7, Sheehan Olver wrote: > > I’m having trouble reading the formulae, but I guess its a nonlinear > PDE in 3D? Right now the package can only do nonlinear ODEs and linear PDEs > on rectangles and disks. We’ll hopefully eventually extend it to nonlinear > PDEs, and 3D PDEs. > > > > > >> On 17 Sep 2015, at 11:40 am, Luke Stagner <[email protected] <javascript:>> >> wrote: >> >> Can this package be used to solve the Grad-Shafranov equation >> <https://en.wikipedia.org/wiki/Grad%E2%80%93Shafranov_equation>? >> >> >> On Wednesday, September 16, 2015 at 3:33:22 PM UTC-7, Sheehan Olver wrote: >> >> ApproxFun is a package for approximating and solving differential equations. >> ApproxFun v0.0.8 Adds (experimental) support for solving nonlinear ODEs, >> using Newton iteration and automatic differentiation. The following example >> solves and plots a singularly perturbed nonlinear two-point boundary value >> problem >> >> x=Fun() >> u0=0.x # The initial guess for Newton iteration >> >> N=u->[u[-1.]-1.,u[1.]+0.5,0.001u''+6*(1-x^2)*u'+u^2-1.] >> u=newton(N,u0) >> ApproxFun.plot(u) # Requires PyPlot or Gadfly >> >> >> Note: previous support for approximating functions on a disk has been moved >> to a separate package: >> >> https://github.com/ApproxFun/DiskFun.jl >> <https://github.com/ApproxFun/DiskFun.jl> >> >> And this will be the last version to support Julia 0.3! >> >
