Add StrangMarchuk second-order symmetric operator splitting

[ChrisRackauckas-Claude]

Summary

Implements the classical Strang-Marchuk ABA splitting scheme as requested in #10. This is a second-order symmetric operator splitting algorithm that achieves higher accuracy than the first-order Lie-Trotter-Godunov scheme through symmetry.

For two operators A and B, the scheme performs:

• A(dt/2) -> B(dt) -> A(dt/2)

Changes

• Added StrangMarchuk algorithm struct in src/solver.jl
• Added StrangMarchukCache cache struct
• Implemented init_cache and advance_solution_to! for the ABA scheme
• Exported StrangMarchuk from the main module
• Extended existing tests to also cover StrangMarchuk

References

• G. Strang, On the construction and comparison of difference schemes, SIAM Journal on Numerical Analysis, 5 (1968), pp. 506-517
• G. I. Marchuk, On the theory of the splitting-up method, in Numerical Solution of Partial Differential Equations-II, Academic Press, 1971, pp. 469-500

Closes #10

Test plan

• All existing tests pass with StrangMarchuk included in the test matrix
• Tests run locally with Pkg.test() - 369 tests pass
• CI passes

cc @ChrisRackauckas

🤖 Generated with Claude Code

[ChrisRackauckas]

rebase

[oameye]

Hey, this is exactly within me needs at the moment. I know it are busy times with the OrdinaryDiffEq v8 release, but can I help to move this forward?

[termi-official]

I did the first big refactoring of the internals with the last release (v0.3) of this package, but we need another round of refactoring to reuse more of the new OrdinaryDiffEqCore infrastructure from the latest release (OrdinaryDiffEq v7).

This brach does unfurtunately not work anymore due to the latest changes (and there were some issues anyway), but you can make a PR to implement and test Strang-Marchuk if you want.

[termi-official]

Superseded by #73