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Switch NLSolve to BracketingNonlinearSolve for stability detection #180

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ChrisRackauckas merged 1 commit into from
Mar 23, 2026
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Switch NLSolve to BracketingNonlinearSolve for stability detection #180

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4 changes: 2 additions & 2 deletions Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -4,14 +4,14 @@ authors = ["Chris Rackauckas <accounts@chrisrackauckas.com>"]
version = "2.50.0"

[deps]
BracketingNonlinearSolve = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e"
CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
DiffEqNoiseProcess = "77a26b50-5914-5dd7-bc55-306e6241c503"
Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
RootedTrees = "47965b36-3f3e-11e9-0dcf-4570dfd42a8c"
Expand All @@ -22,6 +22,7 @@ StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
[compat]
BVProblemLibrary = "0.1"
BoundaryValueDiffEq = "5"
BracketingNonlinearSolve = "1"
CommonSolve = "0.2"
DDEProblemLibrary = "0.1"
DelayDiffEq = "5.20"
Expand All @@ -31,7 +32,6 @@ Distributed = "1.9"
ExplicitImports = "1.14.0"
LinearAlgebra = "1.9"
Logging = "1.9"
NLsolve = "4.5"
NonlinearSolve = "3.13, 4"
ODEProblemLibrary = "0.1"
OrdinaryDiffEq = "6"
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6 changes: 3 additions & 3 deletions src/DiffEqDevTools.jl
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Expand Up @@ -5,14 +5,14 @@ using RecipesBase: RecipesBase, @recipe, @series
using RecursiveArrayTools: RecursiveArrayTools, recursive_mean, vecvecapply
using DiffEqNoiseProcess: DiffEqNoiseProcess, NoiseGrid, NoiseWrapper
using StructArrays: StructArrays, StructArray
using NLsolve: NLsolve, nlsolve
using BracketingNonlinearSolve: BracketingNonlinearSolve, Bisection
using LinearAlgebra: LinearAlgebra, norm, I, /, \
using RootedTrees: RootedTrees, RootedTreeIterator, RungeKuttaMethod, residual_order_condition
using Distributed: Distributed
using Statistics: Statistics, mean, std
using SciMLBase: SciMLBase, DAEProblem, DESolution, EnsembleProblem, EnsembleSolution,
EnsembleThreads, NonlinearProblem, ODEProblem, ReturnCode, SDDEProblem,
SDEProblem, remake
EnsembleThreads, IntervalNonlinearProblem, NonlinearProblem,
ODEProblem, ReturnCode, SDDEProblem, SDEProblem, remake
using CommonSolve: init, solve, step!

import Base: length, convert, transpose
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43 changes: 29 additions & 14 deletions src/tableau_info.jl
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Expand Up @@ -70,11 +70,22 @@ function stability_region(
tab_or_alg::Union{ODERKTableau, AbstractODEAlgorithm};
initial_guess = -3.0, kw...
)
residual! = function (resid, x)
return resid[1] = abs(stability_region(x[1], tab_or_alg)) - 1
f = (x, p) -> abs(stability_region(x, tab_or_alg)) - 1
T = typeof(initial_guess)
# Bracket between a point near 0 (inside stability region) and a point
# far from 0 (outside stability region). Solvers are 0-stable (|r(0)|=1)
# and not ∞-stable, so a sign change must exist between these points.
near_zero = sign(initial_guess) * one(T) / T(10)
far = initial_guess * T(10)
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@oscardssmith oscardssmith Mar 23, 2026

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is 10 big enough to actually find a root?

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@ChrisRackauckas ChrisRackauckas Mar 23, 2026

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The only method that this doesn't work on is Chebyshev methods, which would fail for other reasons because of its adaptivity of building its tableau. So it's good enough, we can make this open ended another way in the future if someone actually cares, but as a dev tool, good enough.

left, right = minmax(near_zero, far)
if f(left, nothing) * f(right, nothing) >= 0
# No sign change on same side of 0 (e.g. A-stable methods).
# Try bracket spanning 0: boundary is at z=0 for A-stable methods.
left, right = minmax(far, -near_zero)
end
sol = nlsolve(residual!, [initial_guess]; kw...)
return sol.zero[1]
prob = IntervalNonlinearProblem{false}(f, (left, right))
sol = solve(prob, Bisection(); kw...)
return sol.u
end

"""
Expand All @@ -90,11 +101,13 @@ function imaginary_stability_interval(
initial_guess = length(tab) - one(eltype(tab.A)),
kw...
)
residual! = function (resid, x)
return resid[1] = abs(stability_region(im * x[1], tab)) - 1
end
sol = nlsolve(residual!, [initial_guess]; kw...)
return sol.zero[1]
f = (x, p) -> abs(stability_region(im * x, tab)) - 1
T = typeof(initial_guess)
near_zero = one(T) / T(10)
far = initial_guess * T(10)
prob = IntervalNonlinearProblem{false}(f, (near_zero, far))
sol = solve(prob, Bisection(); kw...)
return sol.u
end

"""
Expand All @@ -110,11 +123,13 @@ function imaginary_stability_interval(
initial_guess = 20.0,
kw...
)
residual! = function (resid, x)
return resid[1] = abs(stability_region(im * x[1], alg)) - 1
end
sol = nlsolve(residual!, [initial_guess]; kw...)
return sol.zero[1]
f = (x, p) -> abs(stability_region(im * x, alg)) - 1
T = typeof(initial_guess)
near_zero = one(T) / T(10)
far = initial_guess * T(10)
prob = IntervalNonlinearProblem{false}(f, (near_zero, far))
sol = solve(prob, Bisection(); kw...)
return sol.u
end

function RootedTrees.residual_order_condition(
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