Complex Number support

[xtalax]

These are currently unsupported, see #80 for example code

[curio-sitas]

Any news on Complex numbers support ?

[xtalax]

The more people ask for it, the higher priority it gets. I think that MTK is real based but there are tricks you can use to solve complex systems, I'd expect those would work here too but I am unfamiliar with the technique

[curio-sitas]

The more people ask for it, the higher priority it gets. I think that MTK is real based but there are tricks you can use to solve complex systems, I'd expect those would work here too but I am unfamiliar with the technique

Yes, you can eventually split up your system in real and imaginary differential system, but it can be rather tidious

[xtalax]

I can try to do this automatically perhaps

[aplund]

I'm not sure if it's helpful for this or not, but I believe this is a test case of sorts:

module Schro

using ModelingToolkit
using MethodOfLines

@variables t, x
@variables u(..)::Complex

Dx = Differential(x)
Dt = Differential(t)

equation = Dt(u(t,x)) ~ -im*(1/2)*(Dx^2)(u(t,x))

tmax = 50.0
xmax = π
xmin = -xmax

domains=[
    t ∈ (0.0, tmax),
    x ∈ (xmin,xmax)
]

# Exact solution: cos(x/2) e^{-i t/8) + cos(3x/2) e^{-i 9/8 t)

boundary_conditions = [
    u(0.0,x) ~ cos(x/2) + cos(3*x/2),
    u(t,xmin) ~ 0,
    u(t,xmax) ~ 0
]

@named system = PDESystem(
    equation,
    boundary_conditions,
    domains,
    [t, x],
    [u(t,x)]
)

dx=0.1
discretization = MOLFiniteDifference([x => dx], t; approx_order = 2)
problem = discretize(system, discretization)
sol = solve(problem, Tsit5())

end

The error I get now looks like this:

ERROR: LoadError: MethodError: no method matching operation(::Complex{Num})

Closest candidates are:
  operation(::Symbolics.ArrayOp)
   @ Symbolics ~/.julia/packages/Symbolics/gBKZv/src/arrays.jl:93
  operation(::SymbolicUtils.BasicSymbolic)
   @ SymbolicUtils ~/.julia/packages/SymbolicUtils/ssQsQ/src/types.jl:101
  operation(::PolyForm)
   @ SymbolicUtils ~/.julia/packages/SymbolicUtils/ssQsQ/src/polyform.jl:184
  ...

Stacktrace:
 [1] chain_flatten_array_variables(dvs::Vector{Complex{Num}})
   @ PDEBase ~/.julia/packages/PDEBase/aRCcl/src/make_pdesys_compatible.jl:6
 [2] make_pdesys_compatible(pdesys::PDESystem)
   @ PDEBase ~/.julia/packages/PDEBase/aRCcl/src/make_pdesys_compatible.jl:32
 [3] symbolic_discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
   @ PDEBase ~/.julia/packages/PDEBase/aRCcl/src/symbolic_discretize.jl:10
 [4] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}; analytic::Nothing, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ PDEBase ~/.julia/packages/PDEBase/aRCcl/src/discretization_state.jl:58
 [5] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
   @ PDEBase ~/.julia/packages/PDEBase/aRCcl/src/discretization_state.jl:55
 [6] top-level scope
   @ ~/Work/00Projects/AndersonLocalBohm/julia/schro.jl:41
 [7] include(fname::String)
   @ Base.MainInclude ./client.jl:478
 [8] top-level scope
   @ REPL[28]:1
in expression starting at /home/lund/Work/00Projects/AndersonLocalBohm/julia/schro.jl:1