GlobalDiffEq: add the Makazaga-Murua MM5GEE solver - #3955
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This was referenced Jul 18, 2026
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Carries SciML/GlobalDiffEq.jl#56 (GlobalAdjoint, adjoint_error_estimate; Cao and Petzold 2004, closes SciML/GlobalDiffEq.jl#4) into the monorepo, restructured as the package extension GlobalDiffEqSciMLSensitivityExt on SciMLSensitivity + QuadGK weakdeps. sensealg defaults to nothing and resolves to QuadratureAdjoint(autojacvec = true) when the extension loads; solving without the extension raises an instructive error. Public API and semantics otherwise match the original PR. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
Implements the explicit general linear methods with built-in global error estimation from Constantinescu (2016), SIAM J. Numer. Anal. 54(6) (arXiv:1503.05166; PETSc's TSGLEE23/TSGLEE24/TSGLEE35), addressing SciML/GlobalDiffEq.jl#6 and SciML/GlobalDiffEq.jl#22, as proper OrdinaryDiffEqCore algorithms. The methods propagate the partitioned state (y, ε) where ε is an asymptotically correct global error estimate; solve/init on plain ODEProblems transparently extend to the ArrayPartition form and global_error_estimate(sol) extracts the estimates. The per-step ε increment is an asymptotically correct local error estimate driving standard step-size adaptivity. The paper's method A4 is defective as printed (violates b·c = 1/2, converges at order 1, absent from PETSc) and is deliberately not implemented. Verified locally on the unstable Prince42 problem: solution orders 2/2/3, estimate accuracy orders 3/3/4, est/true-error ratio 1.00. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
Adds the DOPRI5-based order-5 scheme with cheap global error estimation of Makazaga and Murua (BIT 43, 2003) as another tableau in the GLEE general linear framework (SciML/GlobalDiffEq.jl#6, the coefficient- complete published representative of the Dormand-Duckers-Prince RK triple family). Stages 1-7 are the standard DOPRI5 stages, three extra stages propagate an order-6 companion solution, and a generic solution-stage FSAL detection reuses stage 7's evaluation for fsallast, giving exactly 9 function evaluations per step (verified by an nf accounting test). The tableau was verified with exact rational arithmetic against the order and independency conditions. Verified locally on the unstable Prince42 problem: solution order 5, estimate accuracy order 6, est/true-error ratio 1.04, 9.01 f-evals/step. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
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Ignore this PR until it has been reviewed by @ChrisRackauckas.
Stacked on #3954 (GLEE solvers), itself stacked on #3953 (adjoint). #3929 (repo transfer) has merged and this branch is rebased onto
master; only the top commit is new here. Merge the base PRs first.Summary
Adds
MM5GEE— the Makazaga–Murua (BIT Numerical Mathematics 43, 2003) Dormand–Prince-based order-5 scheme with cheap global error estimation — as another tableau in the GLEE general-linear framework from the previous PR. This is the coefficient-complete published representative of the Dormand–Duckers–Prince "Runge–Kutta triples" family (SciML/GlobalDiffEq.jl#6): stages 1–7 are the standard DOPRI5 stages, three extra stages propagate an order-6 companion solution, and their difference is an asymptotically correct estimate of the DOPRI5 solution's global error.U[:,2] = 1 − μ, second output rowb̄ − b), so it reuses the whole GLEE cache/stepping infrastructure.Σb̄μ = Σb̄cμ = Σb̄Aμ = Σb̄μ² = 0) before implementation.f(y_{n+1})and reuses it forfsallast, giving exactly the paper's 9 function evaluations per step (verified by annfaccounting test).The higher-order Dormand–Prince triples and the Macdougall–Verner order 7/8 estimators only have coefficients in paywalled sources; this method covers the family with published, machine-verified coefficients.
Version 1.5.0.
Validation (run locally)
ODEDIFFEQ_TEST_GROUP=Core julia --project=lib/GlobalDiffEq -e 'using Pkg; Pkg.test()': pass — Basic 1/1, traits 3/3, Adjoint 14/14, GLEE solvers 37/37, BigFloat 2/2ODEDIFFEQ_TEST_GROUP=QA julia --project=lib/GlobalDiffEq -e 'using Pkg; Pkg.test()': pass — 22 passed, 1 pre-existing declared broken🤖 Generated with Claude Code
https://claude.ai/code/session_01MfUh8tgp3iBmMv9nkBqoyY