Multirate: add MRI-GARK-ERK45a (4th-order explicit)#3751
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singhharsh1708 wants to merge 2 commits into
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Multirate: add MRI-GARK-ERK45a (4th-order explicit)#3751singhharsh1708 wants to merge 2 commits into
singhharsh1708 wants to merge 2 commits into
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June 13, 2026 00:21
Adds the 3rd-order explicit MRI-GARK method of Sandu 2019 (coefficients from SUNDIALS). Unifies all MRI-GARK methods onto one general formulation: per-stage sub-interval (Δc) integration with τ-dependent coupling ω=W0+W1·τ and an explicit RK inner solver (RK2 for ERK22a/b, RK3 for ERK33a), with an embedded lower-order error estimate. Convergence verified: ERK22a/b order 2, ERK33a order 3 (IIP + OOP). Bump 2.3.0 -> 2.4.0.
Adds the 4th-order explicit MRI-GARK method of Sandu 2019 (coefficients from SUNDIALS) — completing the explicit MRI-GARK family (orders 2/3/4) in the unified formulation. Adds an RK4 inner path (q=4) and a τ-dependent embedded coupling (Wemb0+Wemb1·τ) for the order-3 error estimate. Convergence verified: order 4 (IIP + OOP). Bump 2.4.0 -> 2.5.0.
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Stacked on #3747 — the first commit in this PR is #3747 (ERK33a + the unified MRI-GARK formulation); please review that one first. Once #3747 merges, this rebases down to a single ERK45a commit.
Adds MRIGARKERK45a, the 4th-order explicit MRI-GARK method of Sandu 2019, completing the explicit MRI-GARK family (orders 2/3/4) in the unified W-form. Coefficients transcribed from SUNDIALS ARKODE.
What it needed
The general formulation from #3747 already supported it — only two small additions:
q = 4) in the substage integrator.Wemb0 + Wemb1·τ) — ERK45a's embedding row has linear-in-τ terms, unlike ERK33a's constant one — for the order-3 error estimate.5 fast stages (Δc = 1/5 each). Demonstrates the framework generalizes: higher orders drop in as a new tableau + inner order.
Tests
Convergence verified — order 4 (IIP + OOP); full multirate suite green (MRI-GARK 28 tests). Version 2.4.0 → 2.5.0.