refactor(SymplecticRK): migrate drift-kick methods to generic Symplec…

[singhharsh1708]

🚀 SymplecticRK Refactor: Generic Tableau-Based Implementation

This PR introduces a major refactor of the Symplectic Runge-Kutta (SymplecticRK) implementation by replacing multiple per-method implementations with a generic, tableau-driven design.

The previous implementation had significant duplication across methods, with separate cache structs and perform_step! implementations for each algorithm. Since all symplectic methods follow the same drift–kick pattern, this refactor unifies them under a single abstraction.

At the core of this change is the introduction of a generic SymplecticTableau structure that stores method coefficients (a, b) as NTuples. This replaces all per-method constant cache structs while preserving the exact numerical behavior of each algorithm.

The caching system has been simplified by replacing multiple cache types (like Symplectic2Cache, Symplectic3Cache, etc.) with a single SymplecticGenericCache. This significantly reduces boilerplate and makes the system easier to maintain.

The biggest improvement comes from replacing ~20 different perform_step! implementations with just two generic versions (OOP and IIP). These implementations are fully driven by the tableau coefficients and follow a unified loop structure:

for i in 1:N
    u  += dt * b[i] * ku   # drift
    kdu = f1(du, u, ...)
    du += dt * a[i] * kdu  # kick
    ku  = f2(du, u, ...)
end

This abstraction captures the exact structure shared by all symplectic integrators, making the code both mathematically clear and extensible.

Additionally, algorithm dispatch has been simplified using lightweight _symplectic_tableau mappings, where each algorithm maps to its tableau in a single line.

A bug in the CandyRoz4 implementation was also fixed, where it previously used an incorrect cache (McAte4 instead of CandyRoz4).

Impact

• symplectic_perform_step.jl reduced from ~2183 lines to ~340 lines
• symplectic_caches.jl reduced from ~554 lines to ~175 lines
• symplectic_tableaus.jl reduced from ~817 lines to ~430 lines

This results in a significant reduction in code duplication and improves readability, maintainability, and extensibility.

Testing

All tests pass successfully:

• Convergence tests passing (with a few pre-existing broken cases)
• SymplecticRK tests: 160/160 passing
• JET tests passing
• Aqua QA checks passing (including fix for unbound type parameters)

Pre-existing allocation test issues remain unchanged.

Summary

This refactor transforms the SymplecticRK implementation from a method-specific design into a fully generic, coefficient-driven system. It simplifies the codebase, removes redundancy, and aligns the implementation more closely with the mathematical structure of symplectic integrators.

[ChrisRackauckas]

not specialized