Redesign default ODE solver to be type-grounded and lazy

src/derivative_wrappers.jl

@@ -284,7 +284,6 @@ function build_jac_config(alg, f::F1, uf::F2, du1, uprev, u, tmp, du2,
 
         if alg_autodiff(alg) isa AutoForwardDiff
             _chunksize = get_chunksize(alg) === Val(0) ? nothing : get_chunksize(alg) # SparseDiffEq uses different convection...
-
             T = if standardtag(alg)
                 typeof(ForwardDiff.Tag(OrdinaryDiffEqTag(), eltype(u)))
             else

src/solve.jl

@@ -532,11 +532,13 @@
     integrator
 end
 
 function DiffEqBase.__init(prob::ODEProblem, ::Nothing, args...; kwargs...)
-    DiffEqBase.__init(prob, DefaultODEAlgorithm(), args...; kwargs...)
+    alg = DiffEqBase.prepare_alg(DefaultODEAlgorithm(), prob.u0, prob.p, prob)
+    DiffEqBase.__init(prob, alg, args...; kwargs...)
 end
 function DiffEqBase.__solve(prob::ODEProblem, ::Nothing, args...; kwargs...)
-    DiffEqBase.__solve(prob, DefaultODEAlgorithm(), args...; kwargs...)
+    alg = DiffEqBase.prepare_alg(DefaultODEAlgorithm(), prob.u0, prob.p, prob)
+    DiffEqBase.__solve(prob, alg, args...; kwargs...)
 end
 
 function DiffEqBase.solve!(integrator::ODEIntegrator)

test/interface/default_solver_tests.jl

@@ -1,4 +1,4 @@
-using OrdinaryDiffEq, Test, LinearSolve
+using OrdinaryDiffEq, Test, LinearSolve, LinearAlgebra, SparseArrays
 
 f_2dlinear = (du, u, p, t) -> (@. du = p * u)
 
@@ -52,10 +52,13 @@ function exrober(du, u, p, t)
       k₂ * y₂^2, ], u[4:end])
 end
 
-for n in (100, 1000)
+for n in (100, 600)
     stiffalg = n < 500 ? 5 : 6
     linsolve = n < 500 ? nothing : KrylovJL_GMRES()
-    prob_ex_rober = ODEProblem(exrober, vcat([1.0,0.0,0.0], ones(n)),(0.0,100.0),(0.04,3e7,1e4))
+    jac_prototype = sparse(I(n+3))
+    jac_prototype[1:3, 1:3] .= 1.0
+
+    prob_ex_rober = ODEProblem(ODEFunction(exrober; jac_prototype), vcat([1.0,0.0,0.0], ones(n)),(0.0,100.0),(0.04,3e7,1e4))
     sol = solve(prob_ex_rober)
     fsol = solve(prob_ex_rober, AutoTsit5(FBDF(;linsolve)))
     # test that default has the same performance as AutoTsit5(Rosenbrock23()) (which we expect it to use for this).