Multirate: add MRI-GARK-ERK33a (3rd-order) + unify MRI-GARK formulation

[singhharsh1708]

Adds MRIGARKERK33a, the 3rd-order explicit MRI-GARK method of Sandu 2019 (SINUM 57:2300–2327), and unifies the MRI-GARK family onto one general formulation. Follow-up to the order-2 MRI-GARK methods.

Formulation

Each stage integrates the fast IVP v' = Δcᵢ·dt·f1(v) + dt·Σⱼ ωᵢⱼ(τ)·f2(z_{j-1}) over its sub-interval, with τ-dependent coupling ωᵢⱼ(τ) = W0[i,j] + W1[i,j]·τ and an explicit-RK inner solver of order q (RK2 for ERK22a/b, RK3 for ERK33a). An embedded lower-order solution gives the adaptive error estimate. Coefficients transcribed from SUNDIALS ARKODE.

Unification

The previous ERK22a/b used a simplified constant-coupling form; all three methods now share one MRIGARKTableau, cache, and perform_step! (IIP + OOP). The ERK22a/b re-expression is behavior-preserving — existing ERK22 tests pass unchanged.

Tests

Convergence verified — ERK22a/b order 2, ERK33a order 3 (both IIP and OOP); full multirate suite green (MRI-GARK 21 tests). Per-step allocations ~16 bytes. Version 2.3.0 → 2.4.0.

Notes for review

• The inner loop branches on q (2 vs 3) to select the RK2/RK3 inner integrator — happy to type-dispatch it if you'd prefer.
• This re-expresses the merged ERK22 in the general form (behavior-preserving); flagging since the diff touches those methods.