Radau methods fail when trying to solve an ODE

[ranocha]

Thanks a lot for your nice package. I observed the following error:

julia> using GeometricIntegrators

julia> n = 20; u0 = randn(n); tspan = (0.0, 10.0); dt = 0.5
0.5

julia> ode = ODEProblem(tspan, dt, u0) do du, t, u, p
           @. du = -u
           return nothing
       end;

julia> # works as expected
       int = GeometricIntegrator(ode, Gauss(2)); integrate(int);

julia> # fails due to an error
       int = GeometricIntegrator(ode, RadauIIA(2)); integrate(int);
ERROR: MethodError: no method matching solve!(::Vector{…}, ::NoSolver, ::GeometricBase.NullSolverState, ::Tuple{…})

Closest candidates are:
  solve!(::SimpleSolvers.LinearSolver{T, LUT}, ::Any...) where {T, LUT<:SimpleSolvers.LU}
   @ SimpleSolvers ~/.julia/packages/SimpleSolvers/5WLrz/src/linear/lu_solver.jl:119
  solve!(::SimpleSolvers.LinearSolver, ::Any...)
   @ SimpleSolvers ~/.julia/packages/SimpleSolvers/5WLrz/src/linear/linear_solvers.jl:123
  solve!(::AbstractArray, ::SimpleSolvers.NonlinearSolver, ::Any)
   @ SimpleSolvers ~/.julia/packages/SimpleSolvers/5WLrz/src/nonlinear/nonlinear_solver.jl:183
  ...

Stacktrace:
  [1] integrate_step!(sol::State{…}, history::OffsetArrays.OffsetVector{…}, params::NullParameters, int::GeometricIntegrator{…})
    @ GeometricIntegrators.Integrators ~/.julia/dev/GeometricIntegrators/src/integrators/rk/integrators_irk.jl:237
  [2] integrate!(solstep::SolutionStep{…}, int::GeometricIntegrator{…})
    @ GeometricIntegratorsBase ~/.julia/packages/GeometricIntegratorsBase/OFpsS/src/integrate.jl:17
  [3] integrate!
    @ ~/.julia/packages/GeometricIntegratorsBase/OFpsS/src/integrate.jl:38 [inlined]
  [4] integrate!(sol::GeometricSolution{…}, int::GeometricIntegrator{…}, n₁::Int64, n₂::Int64; kwargs::@Kwargs{})
    @ GeometricIntegratorsBase ~/.julia/packages/GeometricIntegratorsBase/OFpsS/src/integrate.jl:69
  [5] integrate!
    @ ~/.julia/packages/GeometricIntegratorsBase/OFpsS/src/integrate.jl:59 [inlined]
  [6] #integrate!#36
    @ ~/.julia/packages/GeometricIntegratorsBase/OFpsS/src/integrate.jl:119 [inlined]
  [7] integrate!(sol::GeometricSolution{…}, int::GeometricIntegrator{…})
    @ GeometricIntegratorsBase ~/.julia/packages/GeometricIntegratorsBase/OFpsS/src/integrate.jl:118
  [8] integrate(integrator::GeometricIntegrator{…}; kwargs::@Kwargs{})
    @ GeometricIntegratorsBase ~/.julia/packages/GeometricIntegratorsBase/OFpsS/src/integrate.jl:126
  [9] integrate(integrator::GeometricIntegrator{…})
    @ GeometricIntegratorsBase ~/.julia/packages/GeometricIntegratorsBase/OFpsS/src/integrate.jl:124
 [10] top-level scope
    @ REPL[15]:1
Some type information was truncated. Use `show(err)` to see complete types.

[michakraus]

Thanks a lot for reporting! That's a nice catch.

Fixed in JuliaGNI/GeometricIntegratorsBase.jl@e7e7f80 (awaiting release).