SciML · ChrisRackauckas · Jul 31, 2025 · Jul 31, 2025
diff --git a/docs/make.jl b/docs/make.jl
@@ -1,4 +1,5 @@
-using Documenter, DiffEqBase, SciMLBase, OrdinaryDiffEq, OrdinaryDiffEqBDF, OrdinaryDiffEqCore, StochasticDiffEq, DelayDiffEq, SteadyStateDiffEq, DiffEqCallbacks
+using Documenter, DiffEqBase, SciMLBase, OrdinaryDiffEq, OrdinaryDiffEqBDF,
+      OrdinaryDiffEqCore, StochasticDiffEq, DelayDiffEq, SteadyStateDiffEq, DiffEqCallbacks
 import ODEProblemLibrary,
        SDEProblemLibrary, DDEProblemLibrary, DAEProblemLibrary, BVProblemLibrary
 using Sundials, DASKR
@@ -18,19 +19,19 @@ if isdir(ordinartdiffeq_docs_path)
     # Create the OrdinaryDiffEq API directory in the docs
     ordinary_diffeq_dest = joinpath(@__DIR__, "src", "api", "ordinarydiffeq")
     mkpath(dirname(ordinary_diffeq_dest))
-    
+
     # Copy all the docs from OrdinaryDiffEq.jl
-    cp(ordinartdiffeq_docs_path, ordinary_diffeq_dest, force=true)
-    
+    cp(ordinartdiffeq_docs_path, ordinary_diffeq_dest, force = true)
+
     # Copy the pages.jl file from OrdinaryDiffEq.jl
     ordinary_diffeq_pages_dest = joinpath(@__DIR__, "ordinarydiffeq_pages.jl")
     ordinary_diffeq_pages_file = joinpath(ordinartdiffeq_docs_root, "pages.jl")
-    cp(ordinary_diffeq_pages_file, ordinary_diffeq_pages_dest, force=true)
-    
+    cp(ordinary_diffeq_pages_file, ordinary_diffeq_pages_dest, force = true)
+
     # Copy the common_first_steps.jl file from OrdinaryDiffEq.jl
     common_first_steps_dest = joinpath(@__DIR__, "common_first_steps.jl")
     common_first_steps_file = joinpath(ordinartdiffeq_docs_root, "common_first_steps.jl")
-    cp(common_first_steps_file, common_first_steps_dest, force=true)
+    cp(common_first_steps_file, common_first_steps_dest, force = true)
 end
 
 # Copy StochasticDiffEq.jl documentation
@@ -40,14 +41,14 @@ if isdir(stochasticdiffeq_docs_path)
     # Create the StochasticDiffEq API directory in the docs
     stochastic_diffeq_dest = joinpath(@__DIR__, "src", "api", "stochasticdiffeq")
     mkpath(dirname(stochastic_diffeq_dest))
-    
+
     # Copy all the docs from StochasticDiffEq.jl
-    cp(stochasticdiffeq_docs_path, stochastic_diffeq_dest, force=true)
-    
+    cp(stochasticdiffeq_docs_path, stochastic_diffeq_dest, force = true)
+
     # Copy the pages.jl file from StochasticDiffEq.jl
     stochastic_diffeq_pages_dest = joinpath(@__DIR__, "stochasticdiffeq_pages.jl")
     stochastic_diffeq_pages_file = joinpath(stochasticdiffeq_docs_root, "pages.jl")
-    cp(stochastic_diffeq_pages_file, stochastic_diffeq_pages_dest, force=true)
+    cp(stochastic_diffeq_pages_file, stochastic_diffeq_pages_dest, force = true)
 end
 
 ENV["PLOTS_TEST"] = "true"
@@ -118,13 +119,13 @@ makedocs(
         "https://github.com/SciML/ColPrac/blob/master/README.md",
         "https://github.com/SciML/DiffEqDevTools.jl/blob/master/src/ode_tableaus.jl",
         "https://github.com/SciML/DiffEqProblemLibrary.jl/blob/master/lib/BVProblemLibrary/src/BVProblemLibrary.jl",
-        "https://github.com/SciML/DiffEqProblemLibrary.jl/blob/master/lib/DDEProblemLibrary/src/DDEProblemLibrary.jl",
+        "https://github.com/SciML/DiffEqProblemLibrary.jl/blob/master/lib/DDEProblemLibrary/src/DDEProblemLibrary.jl"
     ],
     doctest = false, clean = true,
     warnonly = [:missing_docs, :docs_block],
     format = Documenter.HTML(assets = ["assets/favicon.ico"],
         canonical = "https://docs.sciml.ai/DiffEqDocs/stable/",
-              size_threshold = 500 * 2^10),
+        size_threshold = 500 * 2^10),
     sitename = "DifferentialEquations.jl",
     authors = "Chris Rackauckas",
     pages = pages)

diff --git a/docs/pages.jl b/docs/pages.jl
@@ -31,7 +31,7 @@ stochastic_diffeq_pages_file = joinpath(@__DIR__, "stochasticdiffeq_pages.jl")
 stochastic_diffeq_pages = []
 if isfile(stochastic_diffeq_pages_file)
     include(stochastic_diffeq_pages_file)
-    
+
     # Transform StochasticDiffEq pages to have the api/stochasticdiffeq prefix
     function transform_stochasticdiffeq_pages(pages_array)
         transformed = []
@@ -49,77 +49,83 @@ if isfile(stochastic_diffeq_pages_file)
         end
         return transformed
     end
-    
+
     stochastic_diffeq_pages = transform_stochasticdiffeq_pages(pages)
 end
 
 pages = Any["index.md",
-    "getting_started.md",
-    "Tutorials" => Any["tutorials/faster_ode_example.md",
-        "tutorials/advanced_ode_example.md",
-        "tutorials/sde_example.md",
-        "tutorials/rode_example.md",
-        "tutorials/dde_example.md",
-        "tutorials/dae_example.md",
-        "tutorials/jump_diffusion.md",
-        "tutorials/bvp_example.md"],
-    "Examples" => Any[
-        "Beginner" => Any["examples/classical_physics.md",
-            "examples/conditional_dosing.md",
-            "examples/kepler_problem.md",
-            "examples/outer_solar_system.md",
-            "examples/min_and_max.md"],
-        "Advanced" => Any["examples/spiking_neural_systems.md",
-            "examples/beeler_reuter.md",
-            "examples/diffusion_implicit_heat_equation.md"]],
-    "Basics" => Any["basics/overview.md",
-        "basics/common_solver_opts.md",
-        "basics/solution.md",
-        "basics/plot.md",
-        "basics/integrator.md",
-        "basics/problem.md",
-        "basics/faq.md",
-        "basics/compatibility_chart.md"],
-    "Problem Types" => Any["types/discrete_types.md",
-        "types/ode_types.md",
-        "types/nonautonomous_linear_ode.md",
-        "types/dynamical_types.md",
-        "types/split_ode_types.md",
-        "types/steady_state_types.md",
-        "types/bvp_types.md",
-        "types/sde_types.md",
-        "types/sdae_types.md",
-        "types/rode_types.md",
-        "types/dde_types.md",
-        "types/sdde_types.md",
-        "types/dae_types.md"],
-    "Solver Algorithms" => Any["solvers/discrete_solve.md",
-        "solvers/ode_solve.md",
-        "solvers/nonautonomous_linear_ode.md",
-        "solvers/dynamical_solve.md",
-        "solvers/split_ode_solve.md",
-        "solvers/steady_state_solve.md",
-        "solvers/bvp_solve.md",
-        "solvers/sde_solve.md",
-        "solvers/sdae_solve.md",
-        "solvers/rode_solve.md",
-        "solvers/dde_solve.md",
-        "solvers/sdde_solve.md",
-        "solvers/dae_solve.md",
-        "solvers/benchmarks.md"],
-    "Additional Features" => Any["features/performance_overloads.md",
-        "features/diffeq_arrays.md",
-        "features/diffeq_operator.md",
-        "features/noise_process.md",
-        "features/linear_nonlinear.md",
-        "features/callback_functions.md",
-        "features/callback_library.md",
-        "features/ensemble.md",
-        "features/io.md",
-        "features/low_dep.md",
-        "features/progress_bar.md"],
-    "External Solver APIs" => Any["api/sundials.md",
-        "api/daskr.md"],
-    "OrdinaryDiffEq.jl API" => ordinary_diffeq_pages,
-    "StochasticDiffEq.jl API" => stochastic_diffeq_pages,
-    "Extra Details" => Any["extras/timestepping.md"]]
+"getting_started.md",
+"Tutorials" => Any[
+    "tutorials/faster_ode_example.md",
+    "tutorials/advanced_ode_example.md",
+    "tutorials/sde_example.md",
+    "tutorials/rode_example.md",
+    "tutorials/dde_example.md",
+    "tutorials/dae_example.md",
+    "tutorials/jump_diffusion.md",
+    "tutorials/bvp_example.md"],
+"Examples" => Any[
+    "Beginner" => Any["examples/classical_physics.md",
+        "examples/conditional_dosing.md",
+        "examples/kepler_problem.md",
+        "examples/outer_solar_system.md",
+        "examples/min_and_max.md"],
+    "Advanced" => Any["examples/spiking_neural_systems.md",
+        "examples/beeler_reuter.md",
+        "examples/diffusion_implicit_heat_equation.md"]],
+"Basics" => Any[
+    "basics/overview.md",
+    "basics/common_solver_opts.md",
+    "basics/solution.md",
+    "basics/plot.md",
+    "basics/integrator.md",
+    "basics/problem.md",
+    "basics/faq.md",
+    "basics/compatibility_chart.md"],
+"Problem Types" => Any[
+    "types/discrete_types.md",
+    "types/ode_types.md",
+    "types/nonautonomous_linear_ode.md",
+    "types/dynamical_types.md",
+    "types/split_ode_types.md",
+    "types/steady_state_types.md",
+    "types/bvp_types.md",
+    "types/sde_types.md",
+    "types/sdae_types.md",
+    "types/rode_types.md",
+    "types/dde_types.md",
+    "types/sdde_types.md",
+    "types/dae_types.md"],
+"Solver Algorithms" => Any[
+    "solvers/discrete_solve.md",
+    "solvers/ode_solve.md",
+    "solvers/nonautonomous_linear_ode.md",
+    "solvers/dynamical_solve.md",
+    "solvers/split_ode_solve.md",
+    "solvers/steady_state_solve.md",
+    "solvers/bvp_solve.md",
+    "solvers/sde_solve.md",
+    "solvers/sdae_solve.md",
+    "solvers/rode_solve.md",
+    "solvers/dde_solve.md",
+    "solvers/sdde_solve.md",
+    "solvers/dae_solve.md",
+    "solvers/benchmarks.md"],
+"Additional Features" => Any[
+    "features/performance_overloads.md",
+    "features/diffeq_arrays.md",
+    "features/diffeq_operator.md",
+    "features/noise_process.md",
+    "features/linear_nonlinear.md",
+    "features/callback_functions.md",
+    "features/callback_library.md",
+    "features/ensemble.md",
+    "features/io.md",
+    "features/low_dep.md",
+    "features/progress_bar.md"],
+"External Solver APIs" => Any[
+    "api/sundials.md",
+    "api/daskr.md"],
+"OrdinaryDiffEq.jl API" => ordinary_diffeq_pages,
+"StochasticDiffEq.jl API" => stochastic_diffeq_pages,
+"Extra Details" => Any["extras/timestepping.md"]]
diff --git a/docs/src/basics/faq.md b/docs/src/basics/faq.md
@@ -12,9 +12,9 @@ For guidelines on debugging ODE solve issues, see
 First of all, don't panic. You may have experienced one of the following warnings:
 
 > dt <= dtmin. Aborting. There is either an error in your model specification or the true solution is unstable.
->
+> 
 > NaN dt detected. Likely a NaN value in the state, parameters, or derivative value caused this outcome.
->
+> 
 > Instability detected. Aborting
 
 These are all pointing to a similar behavior: for some reason or another, the
@@ -572,7 +572,8 @@ though, an `Error: SingularException` is also possible if the linear solver fail
 
 ```julia
 import DifferentialEquations as DE, OrdinaryDiffEq as ODE, LinearSolve
-DE.solve(prob, ODE.Rodas4(linsolve = LinearSolve.KLUFactorization(; reuse_symbolic = false)))
+DE.solve(prob, ODE.Rodas4(linsolve = LinearSolve.KLUFactorization(;
+    reuse_symbolic = false)))
 ```
 
 For more details about possible linear solvers, consult the [LinearSolve.jl documentation](https://docs.sciml.ai/LinearSolve/stable/)

diff --git a/docs/src/basics/integrator.md b/docs/src/basics/integrator.md
@@ -250,7 +250,8 @@ For example, if one wants to iterate but only stop at specific values, one can
 choose:
 
 ```julia
-integrator = DE.init(prob, DE.Tsit5(); dt = 1 // 2^(4), tstops = [0.5], advance_to_tstop = true)
+integrator = DE.init(
+    prob, DE.Tsit5(); dt = 1 // 2^(4), tstops = [0.5], advance_to_tstop = true)
 for (u, t) in tuples(integrator)
     @test t ∈ [0.5, 1.0]
 end

diff --git a/docs/src/basics/plot.md b/docs/src/basics/plot.md
@@ -160,7 +160,8 @@ xy = Plots.plot(sol, plotdensity = 10000, idxs = (1, 2))
 xz = Plots.plot(sol, plotdensity = 10000, idxs = (1, 3))
 yz = Plots.plot(sol, plotdensity = 10000, idxs = (2, 3))
 xyz = Plots.plot(sol, plotdensity = 10000, idxs = (1, 2, 3))
-Plots.plot(Plots.plot(xyzt, xyz), Plots.plot(xy, xz, yz, layout = (1, 3), w = 1), layout = (2, 1))
+Plots.plot(Plots.plot(xyzt, xyz), Plots.plot(xy, xz, yz, layout = (1, 3), w = 1), layout = (
+    2, 1))
 ```
 
 An example using the functions:

diff --git a/docs/src/basics/solution.md b/docs/src/basics/solution.md
@@ -1,6 +1,6 @@
 # [Solution Handling](@id solution)
 
-The solution is an `RecursiveArrayTools.AbstractDiffEqArray`. 
+The solution is an `RecursiveArrayTools.AbstractDiffEqArray`.
 [See RecursiveArrayTools.jl for more information on the interface](https://docs.sciml.ai/RecursiveArrayTools/stable/).
 The following is a more DiffEq-centric explanation of the interface.
 
@@ -19,7 +19,7 @@ derivative at each timestep `du` or the spatial discretization `x`, `y`, etc.
 ## Array Interface
 
 !!! note
-
+    
     In 2023 the linear indexing `sol[i]` was deprecated. It previously had the behavior that
     `sol[i] = sol.u[i]`. However, this is incompatible with standard `AbstractArray` interfaces,
     Since if `A = VectorOfArray([[1,2],[3,4]])` and `A` is supposed to act like `[1 3; 2 4]`,
@@ -50,7 +50,7 @@ will address first by component and lastly by time, and thus
 sol[i, j]
 ```
 
-will be the `i`th component at timestep `j`. Hence, `sol[j][i] == sol[i, j]`. This is done because Julia is column-major, 
+will be the `i`th component at timestep `j`. Hence, `sol[j][i] == sol[i, j]`. This is done because Julia is column-major,
 so the leading dimension should be contiguous in memory. If the independent variables had shape
 (for example, was a matrix), then `i` is the linear index. We can also access
 solutions with shape:
@@ -186,12 +186,14 @@ error state of the solution. Return codes are now implemented as an enum using E
 rather than symbols.
 
 To check if a solution was successful, use:
+
 ```julia
 SciMLBase.successful_retcode(sol)
 ```
 
 !!! warning
-    Previous iterations of the interface suggested using `sol.retcode == :Success`, 
+
+    Previous iterations of the interface suggested using `sol.retcode == :Success`,
     however, that is now not advised because there are more than one return code that can be interpreted
     as successful. For example, `Terminated` is a successful run to a manual termination, and would be missed
     if only checking for Success. Therefore we highly recommend you use `SciMLBase.successful_retcode(sol)` instead.
@@ -214,7 +216,7 @@ following are major return codes to know:
   - `ConvergenceFailure`: The internal implicit solvers failed to converge.
   - `Failure`: General uncategorized failures or errors.
 
-For a complete list of return codes and their properties, see the 
+For a complete list of return codes and their properties, see the
 [SciMLBase ReturnCode documentation](https://docs.sciml.ai/SciMLBase/stable/interfaces/Solutions/#retcodes).
 
 ## Problem-Specific Features

diff --git a/docs/src/examples/beeler_reuter.md b/docs/src/examples/beeler_reuter.md
@@ -93,8 +93,9 @@ end
 The finite-difference Laplacian is calculated in-place by a 5-point stencil. The Neumann boundary condition is enforced.
 
 !!! note
-    For more complex PDE discretizations, consider using [MethodOfLines.jl](https://docs.sciml.ai/MethodOfLines/stable/) 
-    which can automatically generate finite difference discretizations, or [SciMLOperators.jl](https://docs.sciml.ai/SciMLOperators/stable/) 
+
+    For more complex PDE discretizations, consider using [MethodOfLines.jl](https://docs.sciml.ai/MethodOfLines/stable/)
+    which can automatically generate finite difference discretizations, or [SciMLOperators.jl](https://docs.sciml.ai/SciMLOperators/stable/)
     for defining matrix-free linear operators.
 
 ```julia
@@ -632,7 +633,7 @@ function (f::BeelerReuterGpu)(du, u, p, t)
     ny, nx = size(u)
 
     if Δt != 0 || t == 0
-        @cuda blocks=(ny ÷ L, nx ÷ L) threads=(L, L) update_gates_gpu(f.d_u, f.d_XI, f.d_M,
+        @cuda blocks=(ny÷L, nx÷L) threads=(L, L) update_gates_gpu(f.d_u, f.d_XI, f.d_M,
             f.d_H, f.d_J, f.d_D,
             f.d_F, f.d_C, Δt)
         f.t = t
@@ -641,7 +642,7 @@ function (f::BeelerReuterGpu)(du, u, p, t)
     laplacian(f.Δv, u)
 
     # calculate the reaction portion
-    @cuda blocks=(ny ÷ L, nx ÷ L) threads=(L, L) update_du_gpu(
+    @cuda blocks=(ny÷L, nx÷L) threads=(L, L) update_du_gpu(
         f.d_du, f.d_u, f.d_XI, f.d_M,
         f.d_H, f.d_J, f.d_D, f.d_F,
         f.d_C)

diff --git a/docs/src/examples/classical_physics.md b/docs/src/examples/classical_physics.md
@@ -382,7 +382,8 @@ Notice that we get the same results:
 
 ```@example physics
 # Plot the orbit
-Plots.plot(sol2, idxs = (3, 4), title = "The orbit of the Hénon-Heiles system", xaxis = "x",
+Plots.plot(
+    sol2, idxs = (3, 4), title = "The orbit of the Hénon-Heiles system", xaxis = "x",
     yaxis = "y", leg = false)
 ```
 

diff --git a/docs/src/examples/kepler_problem.md b/docs/src/examples/kepler_problem.md
@@ -33,7 +33,9 @@ sol = ODE.solve(prob, ODE.KahanLi6(), dt = 1 // 10);
 Let's plot the orbit and check the energy and angular momentum variation. We know that energy and angular momentum should be constant, and they are also called first integrals.
 
 ```@example kepler
-plot_orbit(sol) = Plots.plot(sol, idxs = (3, 4), lab = "Orbit", title = "Kepler Problem Solution")
+function plot_orbit(sol)
+    Plots.plot(sol, idxs = (3, 4), lab = "Orbit", title = "Kepler Problem Solution")
+end
 
 function plot_first_integrals(sol, H, L)
     Plots.plot(initial_first_integrals[1] .- map(u -> H(u.x[2], u.x[1]), sol.u),

diff --git a/docs/src/features/ensemble.md b/docs/src/features/ensemble.md
@@ -574,7 +574,7 @@ compute covariance matrices similarly:
 
 ```@example ensemble4
 DE.EnsembleAnalysis.timeseries_steps_meancov(sim) # Use the time steps, assume fixed dt
-DE.EnsembleAnalysis.timeseries_point_meancov(sim, 0:(1 // 2^(3)):1, 0:(1 // 2^(3)):1) # Use time points, interpolate
+DE.EnsembleAnalysis.timeseries_point_meancov(sim, 0:(1 // 2 ^ (3)):1, 0:(1 // 2 ^ (3)):1) # Use time points, interpolate
 ```
 
 For general analysis, we can build a `EnsembleSummary` type.