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Trying to get Neumann boundary conditions to work with the Helmholtz equation has been tricky, but this is something I didn't expect.
If an incident wave is normal to the scatterer (d=(0,-1)) then fo…
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Right now dirichlet(::PiecewiseSpace) assumes you want continuity up to first derivative. This only works for second order ODEs, and right now there is no support for telling the order of an ODE. It…
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I think this I've worked this out correctly: Hilbert acting on a PiecewiseSpace consisting of JacobiWeight spaces should have the Cauchy rangespaces be Ultraspherical (i.e. the space of the alternate …
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Right now julia can't have constructors for typealiases with parameters. This is preventing the addition of types to FunctionSpace, since then Chebyshev requires a parameter. If it was its own type …
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Examples:
1) upper triangular operators should use backsubstitution!
2) many operators decouple the even and odd rows/columns (E.g. Ultraspherical Derivative/Conversion). exploiting this hal…
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In solving this differential equation, I get a solution of length 128:
```
dom = [0, 10];
op = @(u) 2*diff(u,3) + u.*diff(u,2);
bc = @(x,u) [u(0); feval(diff(u),0); feval(diff(u),dom(2))-1];
N = …
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I wish I could type
D=Derivative()
B=dirichlet()
x=Fun(identity)
u=[B,D^2+x][1.,0.]
and it chooses the space from x. At the moment, the x is interpreted as Multiplication(x,AnySpace()) so that spac…
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not sure if this is a legitimate issue, but
``` julia
julia> Fun(x->2,d)
ERROR: type: chebyshevtransform: in typeassert, expected Array{Int64,1}, got Array{Float64,1}
in chebyshevtransform at /User…
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Was going through the unicode math symbols and realized they include ⨍ and ⨎. Surely We can use these somehow for writing hilbert?? This would be cool if it worked:
x=Fun(identity)
⨍(exp(x)*sqrt(1…