Fix Multirate FastBroadcast compat and BDF convergence-test KeyError (#3386)

Two independent master test failures:

* OrdinaryDiffEqMultirate pins FastBroadcast = "0.3", but
  OrdinaryDiffEqCore requires FastBroadcast = "1.3", so Pkg.Resolve
  fails immediately. Bump the Multirate compat to "1.3" and bump the
  package version to 1.0.1.

* The QNDF1 + AutoEnzyme + KrylovJL convergence test added by #3373
  passes `reltol = 1.0e-14, abstol = 1.0e-14`. BDF-1's local error
  floor exceeds double-precision near those tolerances, so Newton
  hits ConvergenceFailure on every dt except the finest. Failed
  solutions have an empty `sol.errors` dict, which then makes
  DiffEqDevTools.ConvergenceSimulation crash with
  `KeyError: key :l∞ not found` while iterating keys of the first
  (successful) solution. Drop the tight-tolerance override for this
  BDF case; the tightening from #3373 was only needed to avoid
  LinearSolve's residual-tolerance coupling starving Rosenbrock
  convergence, which is not a problem here. Locally verified:
  QNDF1 + KrylovJL reports final/l2/l∞ order ≈ 1.0–1.17 on both
  prob_ode_linear and prob_ode_2Dlinear (testTol = 0.2).

Co-authored-by: ChrisRackauckas-Claude <accounts@chrisrackauckas.com>
Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: 3 people

lib/OrdinaryDiffEqBDF/test/bdf_convergence_tests.jl

@@ -67,6 +67,11 @@ end
         @test sim.𝒪est[:l2] ≈ 1 atol = testTol
         @test sim.𝒪est[:l∞] ≈ 1 atol = testTol
 
+        # Note: tight reltol/abstol (1e-14) is unusable for BDF-1 because the
+        # method's local error floor exceeds machine precision, causing Newton
+        # ConvergenceFailure on all but the finest dt. Leave reltol/abstol at the
+        # defaults; without the LinearSolve residual-tolerance coupling described in
+        # #3373, QNDF1's observed order already lands near 1 on prob_ode_2Dlinear.
         sim = test_convergence(
             dts,
             prob,
@@ -76,8 +81,7 @@ end
                     function_annotation = Enzyme.Const
                 ),
                 linsolve = LinearSolve.KrylovJL()
-            ),
-            reltol = 1.0e-14, abstol = 1.0e-14
+            )
         )
         @test sim.𝒪est[:final] ≈ 1 atol = testTol
         @test sim.𝒪est[:l2] ≈ 1 atol = testTol

lib/OrdinaryDiffEqMultirate/Project.toml

@@ -1,7 +1,7 @@
 name = "OrdinaryDiffEqMultirate"
 uuid = "d4b830b4-ac80-426b-8507-16693d424963"
 authors = ["singhharsh1708 <hs1663531@gmail.com>"]
-version = "1.0.0"
+version = "1.0.1"
 
 [deps]
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
@@ -17,7 +17,7 @@ SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 Aqua = "0.8.11"
 DiffEqBase = "6.194"
 DiffEqDevTools = "2.44.4"
-FastBroadcast = "0.3"
+FastBroadcast = "1.3"
 JET = "0.9, 0.11"
 MuladdMacro = "0.2"
 OrdinaryDiffEqCore = "3"