GlobalDiffEq: add GLEE23/GLEE24/GLEE35 global-error-estimating solvers#3954
Draft
ChrisRackauckas-Claude wants to merge 2 commits into
Draft
GlobalDiffEq: add GLEE23/GLEE24/GLEE35 global-error-estimating solvers#3954ChrisRackauckas-Claude wants to merge 2 commits into
ChrisRackauckas-Claude wants to merge 2 commits into
Conversation
This was referenced Jul 18, 2026
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>
ChrisRackauckas-Claude
force-pushed
the
globaldiffeq-glee
branch
from
July 22, 2026 08:24
154e1b5 to
97c4bb2
Compare
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Important
Ignore this PR until it has been reviewed by @ChrisRackauckas.
Stacked on #3953 (adjoint). #3929 (repo transfer) has merged and this branch is rebased onto
master; only the top commit is new here. Merge #3953 first.Summary
Adds
GLEE23,GLEE24,GLEE35— the explicit general linear methods with built-in global error estimation of Constantinescu, SIAM J. Numer. Anal. 54(6), 2016 (PETSc'sTSGLEE23/24/35) — as properOrdinaryDiffEqCoresolver algorithms (alg_cache/initialize!/perform_step!). Addresses SciML/GlobalDiffEq.jl#6 and SciML/GlobalDiffEq.jl#22.Design, following the plan in SciML/DifferentialEquations.jl#670 (comment):
(y, ε)in the paper's y-ε general linear form, whereεis an asymptotically correct estimate of the global errory_exact − yat every step.solve/initon a plainODEProblemtransparently extend it toArrayPartitionstate (the "guiding layer" adjusts the user's input);global_error_estimate(sol)(new export) extracts the estimate trajectory.εis an asymptotically correct local error estimate, which drives the standard step-size controllers, so the methods are fully adaptive with the usualabstol/reltolsemantics while the global error estimate comes along for free.glee.c(GLEE35's exact rationals exceedInt64and are constructed asBigIntrationals). The y-ỹ→y-ε form conversion (paper Lemma 4.1) is done at construction. Consistency (ΣB₁ = 1,ΣB₂ = 0,U·[1,0]ᵀ = 1) is preserved exactly.b·c = 1/2and converges at order 1 in a direct test; it is also absent from PETSc — so it was deliberately not implemented.fsalfirstwhen the tableau allows (GLEE23), and dense output gets true endpoint derivatives.GLEE24andGLEE35satisfy both of the paper's decoupling conditions (B·UandB·A·Udiagonal) and are the recommended choices;GLEE23is the cheapest (3 stages).Version 1.4.0.
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 30/30, BigFloat 2/2ODEDIFFEQ_TEST_GROUP=QA julia --project=lib/GlobalDiffEq -e 'using Pkg; Pkg.test()': pass — 22 passed, 1 pre-existing declared brokeny' = y − sin t + cos t, errors grow likeeᵗ), in-place and out-of-place: solution orders 2/2/3 and estimate-accuracy orders 3/3/4 as claimed; est/true-error ratio ≈ 1.00 at the finest fixed step; adaptive solves stay faithful; the integrator interface (init/solve!) works on plain problems.🤖 Generated with Claude Code
https://claude.ai/code/session_01MfUh8tgp3iBmMv9nkBqoyY