juliaapproximation / approxfunexamples Goto Github PK

I was inspired by https://github.com/FourierFlows/FourierFlows.jl, in particular the example they have (https://github.com/FourierFlows/FourierFlows.jl/blob/master/examples/OneDShallowWaterGeostrophicAdjustment.jl) that gets run as part of the documentation stage in GitHub Actions in every commit. The very nice result is https://fourierflows.github.io/FourierFlowsDocumentation/dev/generated/OneDShallowWaterGeostrophicAdjustment/.

Did the same thing with the FastTransforms examples (since the docs are quite sparse), and I'm pretty pleased. The FourierFlows.jl scripts show that docs can be hosted in a separated repository, so probably it's possible for the examples here to be added to the ApproxFun.jl documentation website. Or alternatively, have a separated website repository be built from multiple GitHub sources (the source source and examples source).

running Helmholtz rectangle PDE example on this page

https://github.com/JuliaApproximation/ApproxFunExamples/blob/master/PDEs/Rectangle%20PDEs.ipynb

d = (-1.0..1.0)^2

Δ = Laplacian(d)

@time u = \([Dirichlet(d);Δ+100I], [ones(∂(d));0]; tolerance=1E-5)
plot(u)

gives

MethodError: no method matching Dirichlet(::Interval{Float64})
Closest candidates are:
  Dirichlet() at /Users/abradley/.julia/packages/ApproxFun/wFAIT/src/Operators/functionals/Evaluation.jl:181
  Dirichlet(!Matched::Chebyshev, !Matched::Any) at /Users/abradley/.julia/packages/ApproxFun/wFAIT/src/Spaces/Chebyshev/ChebyshevOperators.jl:128
  Dirichlet(!Matched::TensorSpace{Tuple{ChebyshevDirichlet{1,1,Segment{T},R1},ChebyshevDirichlet{1,1,Segment{T},R2}},D,R} where R where D, !Matched::Any) where {T, R1, R2} at /Users/abradley/.julia/packages/ApproxFun/wFAIT/src/Spaces/Ultraspherical/ContinuousSpace.jl:221

in Blasius and Falkner-Skan.jl
f = (u)->(2.0*D^3*u + 3*u*D^2*u)
df = (u)->(2.0*D^3 + u*D^2 + D^2*u)

Shouldn't it be
df = (u)->(6.0*D^2 + D^2*u + 2*u*D*u)

Other thing is,
global u -= [B; df(u)]\[u(0.);u'(0.);u'(rightendpoint(d))-1.;f(u)]
What is happening in this line of code?

Hello.
Do you currently have support for the heat equation with non-constant coefficients?

or, alternatively,

where u(x,t) is the solution and k(x) is the variable coefficient.

Thank you for considering this question.