I am using the split step method to solve the following equation:

The first 3 terms are straightforward when using the split step method. For the fourth term, I basically need to solve this equation:

after evolving the equation for the first three terms. i.e. I need to repeatedly use `DifferentialEquations.solve`

inside an outer time loop to evolve the solution a single step. This is very slow, unfortunately.

This is a simple example of how this works (I can provide a full MWE if needed but it’s on the longer side)

```
function solve!(...)
# Prepare some stuff
# ...
# Differential Operators
α = 0.1
x_order = 2
D = CenteredDifference(1, x_order, dx, Nx)
Q = PeriodicBC(Float64)
function M!(du, u,p,t)
du = 6*α*D*Q*u.*abs2.(u)
end
for i = 1:Nt-1
@views ψ[:, i+1] .= T(ψ[:, i], dt, M!, ...)
end
return nothing
end #solve
function T(ψ, W, dt, F, F̃, M!)
# Perform some operations in-place on ψ
# Calling this every loop is slow and allocates a lot
prob = ODEProblem(M!, ψ, (0.0, dt))
sol = solve(prob, BS3(), save_everystep = false, dt = dt)
ψ = sol.u[end]
return ψ
end
```

So as you can see, the function `T`

evolves time by a single step, so it performs some operations on `ψ`

then has to solve the ODE. This happens every single time step, so re-initializing the problem and then solving it makes the whole process very time consuming. I made the function `M!`

in place and it helped a bit, but I am stuck at this point.