New solvers

SDE:

• Milstein
• Euler-Heun
• SRKs (Additive)
• Talay (Ito commutative)

Implict:

• BDF
• Rosenbrock methods
• IMEX methods, e.g. http://dx.doi.org/10.1175/mwr-d-13-00132.1

DAE:

• Lots of overlap with Rosenbrock methods, get them in at the same time.
• Standard DAE->ODE conversion (+optional nonlinear projections)
• Set made_jump=True if dconstraint/dz=0
• Mass matrices: work with these or work with constraint functions? Former is a little more general; maybe less efficient in some cases? Also think about traced mass matrices, possibly space-varying (e.g. quasilinear problems), possibly rank-varying.

Symplectic:

• Higher-order symplectic methods
• A lot of the lower-order methods (Stormer-Verlet, Leapfrog, Kick-drift-kick, Semi-implicit Euler) are all essentially the same thing. It would be good to write out something making this explicit, plus maybe add some special variants if you really want a particular variant.

Other:

• Higher-order ERK methods (Verner etc.)
• See also a few of the comments made about DifferentialEquations.jl in this (old) blog post: https://www.stochasticlifestyle.com/comparison-differential-equation-solver-suites-matlab-r-julia-python-c-fortran/

No files, tests, or entry points are named. Start by reviewing the existing solver organization and narrowing this broad wishlist to one unchecked method family, such as Talay, BDF, or higher-order symplectic methods. Use the linked paper or blog post where relevant; completion would require a defined method, implementation scope, and validation criteria.