diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 08753831..8b51f3b8 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -54,7 +54,7 @@ jobs:
           - macos-latest
           - windows-latest
         include:
-          - version: '1.9'
+          - version: '1.11'
             os: ubuntu-latest
     steps:
       - uses: actions/checkout@v4
diff --git a/.github/workflows/Documenter.yml b/.github/workflows/Documenter.yml
index 3d3760e1..602da561 100644
--- a/.github/workflows/Documenter.yml
+++ b/.github/workflows/Documenter.yml
@@ -35,7 +35,7 @@ jobs:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v2
         with:
-          version: '1.9'
+          version: '1.10'
           show-versioninfo: true
       - uses: julia-actions/cache@v2
       - uses: julia-actions/julia-buildpkg@v1
diff --git a/.github/workflows/Downgrade.yml b/.github/workflows/Downgrade.yml
index 0df44435..0d6c0b13 100644
--- a/.github/workflows/Downgrade.yml
+++ b/.github/workflows/Downgrade.yml
@@ -35,7 +35,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.9'
+          - '1.10'
           # - '~1.9.0-0' # including development versions
           # - 'nightly'
         os:
@@ -49,7 +49,7 @@ jobs:
       - uses: julia-actions/cache@v2
       - uses: julia-actions/julia-downgrade-compat@v1
         with:
-          skip: LinearAlgebra,Printf,SparseArrays
+          skip: LinearAlgebra,Printf,SparseArrays,Test
           projects: ., test
       - uses: julia-actions/julia-buildpkg@v1
         env:
diff --git a/Project.toml b/Project.toml
index e772cc52..39301f3f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -25,21 +25,21 @@ TrixiBase = "9a0f1c46-06d5-4909-a5a3-ce25d3fa3284"
 
 [compat]
 BandedMatrices = "1"
-DiffEqBase = "6.143"
-FastBroadcast = "0.2.8, 0.3"
-Interpolations = "0.14.2, 0.15"
+DiffEqBase = "6.157"
+FastBroadcast = "0.3.5"
+Interpolations = "0.15.1"
 LinearAlgebra = "1"
 PolynomialBases = "0.4.15"
 Printf = "1"
-RecipesBase = "1.2"
-RecursiveArrayTools = "3.3"
-Reexport = "1.0"
+RecipesBase = "1.3.4"
+RecursiveArrayTools = "3.27"
+Reexport = "1.2.2"
 Roots = "2.0.17"
-SciMLBase = "2.11"
+SciMLBase = "2.56"
 SimpleUnPack = "1.1"
 SparseArrays = "1"
-StaticArrays = "1"
+StaticArrays = "1.9.7"
 SummationByPartsOperators = "0.5.63"
 TimerOutputs = "0.5.7"
 TrixiBase = "0.1.3"
-julia = "1.9"
+julia = "1.10"
diff --git a/README.md b/README.md
index a8e5762e..66196931 100644
--- a/README.md
+++ b/README.md
@@ -25,15 +25,21 @@ A more detailed documentation can be found [online](https://JoshuaLampert.github
 ## Installation
 
 If you have not yet installed Julia, then you first need to [download Julia](https://julialang.org/downloads/). Please [follow the instructions for your operating system](https://julialang.org/downloads/platform/).
-DispersiveShallowWater.jl works with Julia v1.9 and newer. DispersiveShallowWater.jl is a registered Julia package. Therefore, you can install it by executing the following commands from the Julia REPL
+DispersiveShallowWater.jl works with Julia v1.10 and newer. DispersiveShallowWater.jl is a registered Julia package. Therefore, you can install it by executing the following commands from the Julia REPL
+
 ```julia
 julia> using Pkg
 
-julia> Pkg.add(["DispersiveShallowWater", "OrdinaryDiffEq", "Plots"])
+julia> Pkg.add(["DispersiveShallowWater", "OrdinaryDiffEqTsit5", "Plots"])
 ```
-In addition, this installs the packages [OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl) used for time-integration and [Plots.jl](https://github.com/JuliaPlots/Plots.jl) to visualize the results.
+
+In addition, this installs the packages OrdinaryDiffEqTsit5.jl from [OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl)
+used for time-integration and [Plots.jl](https://github.com/JuliaPlots/Plots.jl) to visualize the results. If you want to use
+other time integration methods than `Tsit5`, you can install the respective subpackage or OrdinaryDiffEq.jl, which will install
+every available solver.
 If you want to use other SBP operators than the default operators that DispersiveShallowWater.jl uses, then you also need [SummationByPartsOperators.jl](https://github.com/ranocha/SummationByPartsOperators.jl),
 which can be installed running
+
 ```julia
 julia> Pkg.add("SummationByPartsOperators")
 ```
@@ -41,19 +47,24 @@ julia> Pkg.add("SummationByPartsOperators")
 ## Usage
 
 In the Julia REPL, first load the package DispersiveShallowWater.jl
+
 ```julia
 julia> using DispersiveShallowWater
 ```
 
 You can run a basic simulation that solves the BBM-BBM equations by executing
+
 ```julia
 julia> include(default_example());
 ```
+
 The result can be visualized by using the package Plots.jl
+
 ```julia
 julia> using Plots
 julia> plot(semi => sol)
 ```
+
 The command `plot` expects a `Pair` consisting of a `Semidiscretization` and an `ODESolution`. The visualization can also be customized, see the [documentation](https://JoshuaLampert.github.io/DispersiveShallowWater.jl/stable/overview#visualize_results)
 for more details. Other examples can be found in the subdirectory [examples/](https://github.com/JoshuaLampert/DispersiveShallowWater.jl/tree/main/examples).
 A list of all examples is returned by running `get_examples()`. You can pass the filename of one of the examples or your own simulation file to `include` in order to run it,
@@ -62,6 +73,7 @@ e.g., `include(joinpath(examples_dir(), "svaerd_kalisch_1d", "svaerd_kalisch_1d_
 ## Referencing
 
 You can directly refer to DispersiveShallowWater.jl as
+
 ```bibtex
 @misc{lampert2023dispersive,
   title={{D}ispersive{S}hallow{W}ater.jl: {S}tructure-preserving numerical
diff --git a/benchmark/Project.toml b/benchmark/Project.toml
index cf3a822b..d55cf819 100644
--- a/benchmark/Project.toml
+++ b/benchmark/Project.toml
@@ -1,9 +1,11 @@
 [deps]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
-OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+OrdinaryDiffEqLowStorageRK = "b0944070-b475-4768-8dec-fb6eb410534d"
+OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
 SummationByPartsOperators = "9f78cca6-572e-554e-b819-917d2f1cf240"
 
 [compat]
 BenchmarkTools = "1"
-OrdinaryDiffEq = "6.49.1"
+OrdinaryDiffEqLowStorageRK = "1"
+OrdinaryDiffEqTsit5 = "1"
 SummationByPartsOperators = "0.5.63"
diff --git a/docs/Project.toml b/docs/Project.toml
index 76e53476..3821d09d 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,7 +1,7 @@
 [deps]
 Changelog = "5217a498-cd5d-4ec6-b8c2-9b85a09b6e3e"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 SummationByPartsOperators = "9f78cca6-572e-554e-b819-917d2f1cf240"
 TrixiBase = "9a0f1c46-06d5-4909-a5a3-ce25d3fa3284"
@@ -9,7 +9,7 @@ TrixiBase = "9a0f1c46-06d5-4909-a5a3-ce25d3fa3284"
 [compat]
 Changelog = "1"
 Documenter = "1"
-OrdinaryDiffEq = "6.49.1"
+OrdinaryDiffEqTsit5 = "1"
 Plots = "1.9"
 SummationByPartsOperators = "0.5.41"
 TrixiBase = "0.1.1"
diff --git a/docs/src/development.md b/docs/src/development.md
index 9299bf9d..2ace72c4 100644
--- a/docs/src/development.md
+++ b/docs/src/development.md
@@ -19,7 +19,7 @@ cd DispersiveShallowWater
 mkdir run
 cd run
 julia --project=. -e 'using Pkg; Pkg.develop(PackageSpec(path=".."))' # Install local DispersiveShallowWater.jl clone
-julia --project=. -e 'using Pkg; Pkg.add(["OrdinaryDiffEq", "Plots", "SummationByPartsOperators"])' # Install additional packages
+julia --project=. -e 'using Pkg; Pkg.add(["OrdinaryDiffEqTsit5", "Plots", "SummationByPartsOperators"])' # Install additional packages
 ```
 
 If you use other packages for executing DispersiveShallowWater.jl, you can add them to the project in the `run`
diff --git a/docs/src/index.md b/docs/src/index.md
index 9fd925ed..1b4d8028 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -24,15 +24,21 @@ Fully discrete entropy-conservative methods can be obtained by using the [relaxa
 ## Installation
 
 If you have not yet installed Julia, then you first need to [download Julia](https://julialang.org/downloads/). Please [follow the instructions for your operating system](https://julialang.org/downloads/platform/).
-DispersiveShallowWater.jl works with Julia v1.9 and newer. DispersiveShallowWater.jl is a registered Julia package. Therefore, you can install it by executing the following commands from the Julia REPL
+DispersiveShallowWater.jl works with Julia v1.10 and newer. DispersiveShallowWater.jl is a registered Julia package. Therefore, you can install it by executing the following commands from the Julia REPL
+
 ```julia
 julia> using Pkg
 
-julia> Pkg.add(["DispersiveShallowWater", "OrdinaryDiffEq", "Plots"])
+julia> Pkg.add(["DispersiveShallowWater", "OrdinaryDiffEqTsit5", "Plots"])
 ```
-In addition, this installs the packages [OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl) used for time-integration and [Plots.jl](https://github.com/JuliaPlots/Plots.jl) to visualize the results.
+
+In addition, this installs the packages OrdinaryDiffEqTsit5.jl from [OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl)
+used for time-integration and [Plots.jl](https://github.com/JuliaPlots/Plots.jl) to visualize the results. If you want to use
+other time integration methods than `Tsit5`, you can install the respective subpackage or OrdinaryDiffEq.jl, which will install
+every available solver.
 If you want to use other SBP operators than the default operators that DispersiveShallowWater.jl uses, then you also need [SummationByPartsOperators.jl](https://github.com/ranocha/SummationByPartsOperators.jl),
 which can be installed running
+
 ```julia
 julia> Pkg.add("SummationByPartsOperators")
 ```
@@ -40,19 +46,24 @@ julia> Pkg.add("SummationByPartsOperators")
 ## Usage
 
 In the Julia REPL, first load the package DispersiveShallowWater.jl
+
 ```julia
 julia> using DispersiveShallowWater
 ```
 
 You can run a basic simulation that solves the BBM-BBM equations by executing
+
 ```julia
 julia> include(default_example());
 ```
+
 The result can be visualized by using the package Plots.jl
+
 ```julia
 julia> using Plots
 julia> plot(semi => sol)
 ```
+
 The command `plot` expects a `Pair` consisting of a [`Semidiscretization`](@ref) and an `ODESolution`. The visualization can also be customized, see the [documentation](@ref visualize_results)
 for more details. Other examples can be found in the subdirectory [examples/](https://github.com/JoshuaLampert/DispersiveShallowWater.jl/tree/main/examples).
 A list of all examples is returned by running [`get_examples()`](@ref). You can pass the filename of one of the examples or your own simulation file to `include` in order to run it,
@@ -61,6 +72,7 @@ e.g., `include(joinpath(examples_dir(), "svaerd_kalisch_1d", "svaerd_kalisch_1d_
 ## Referencing
 
 You can directly refer to DispersiveShallowWater.jl as
+
 ```bibtex
 @misc{lampert2023dispersive,
   title={{D}ispersive{S}hallow{W}ater.jl: {S}tructure-preserving numerical
diff --git a/docs/src/overview.md b/docs/src/overview.md
index 64adf57f..e404b875 100644
--- a/docs/src/overview.md
+++ b/docs/src/overview.md
@@ -27,7 +27,7 @@ In order to conduct a numerical simulation with DispersiveShallowWater.jl, we pe
 First, we load the necessary libraries:
 
 ```@example overview
-using DispersiveShallowWater, OrdinaryDiffEq
+using DispersiveShallowWater, OrdinaryDiffEqTsit5
 ```
 
 ## Define physical setup
@@ -106,7 +106,9 @@ is a nonlinear invariant and should be constant over time as well. During the si
 
 Finally, the `ode` can be `solve`d using the interface from [OrdinaryDiffEq.jl](https://github.com/SciML/OrdinaryDiffEq.jl). This means, we can specify a time-stepping
 scheme we want to use the tolerances for the adaptive time-stepping and the time values, where the solution values should be saved. In this case, we use the adaptive
-explicit Runge-Kutta method `Tsit5` by Tsitouras of order 5(4). Here, we save the solution at 100 equidistant points.
+explicit Runge-Kutta method `Tsit5` by Tsitouras of order 5(4), which is implemented in the subpackage OrdinaryDiffEqTsit5.jl. If you want to use other time-stepping
+schemes, you can install the respective subpackage or the whole package OrdinaryDiffEq.jl, which will install every available solver.
+Here, we save the solution at 100 equidistant points.
 
 ```@example overview
 tspan = (0.0, 25.0)
@@ -214,7 +216,6 @@ nothing # hide
 
 ![analysis callback relaxation](analysis_callback_relaxation.png)
 
-
 ## [Customize solver](@id customize_solver)
 
 In the semidiscretization created above, we used the default SBP operators, which are periodic finite difference operators. Using different SBP operators for the
@@ -307,4 +308,3 @@ and [plot_examples.jl](https://github.com/JoshuaLampert/2023-master-thesis/blob/
     Ranocha, Sayyari, Dalcin, Parsani, Ketcheson (2020):
     Relaxation Runge–Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier–Stokes Equations
     [DOI: 10.1137/19M1263480](https://doi.org/10.1137/19M1263480)
-
diff --git a/examples/bbm_1d/bbm_1d_basic.jl b/examples/bbm_1d/bbm_1d_basic.jl
index 70be29ca..d619e3c1 100644
--- a/examples/bbm_1d/bbm_1d_basic.jl
+++ b/examples/bbm_1d/bbm_1d_basic.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/bbm_1d/bbm_1d_fourier.jl b/examples/bbm_1d/bbm_1d_fourier.jl
index 92b7146e..57642a26 100644
--- a/examples/bbm_1d/bbm_1d_fourier.jl
+++ b/examples/bbm_1d/bbm_1d_fourier.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: fourier_derivative_operator
 
diff --git a/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl b/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl
index 266e9e8e..39e78b3c 100644
--- a/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl
+++ b/examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/bbm_1d/bbm_1d_manufactured.jl b/examples/bbm_1d/bbm_1d_manufactured.jl
index a738a8cd..15627872 100644
--- a/examples/bbm_1d/bbm_1d_manufactured.jl
+++ b/examples/bbm_1d/bbm_1d_manufactured.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/bbm_1d/bbm_1d_relaxation.jl b/examples/bbm_1d/bbm_1d_relaxation.jl
index 7699e976..59f11d9b 100644
--- a/examples/bbm_1d/bbm_1d_relaxation.jl
+++ b/examples/bbm_1d/bbm_1d_relaxation.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/bbm_bbm_1d/bbm_bbm_1d_basic.jl b/examples/bbm_bbm_1d/bbm_bbm_1d_basic.jl
index 82c1c7e7..ecdcaba2 100644
--- a/examples/bbm_bbm_1d/bbm_bbm_1d_basic.jl
+++ b/examples/bbm_bbm_1d/bbm_bbm_1d_basic.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/bbm_bbm_1d/bbm_bbm_1d_basic_reflecting.jl b/examples/bbm_bbm_1d/bbm_bbm_1d_basic_reflecting.jl
index 89214343..bcdec7fb 100644
--- a/examples/bbm_bbm_1d/bbm_bbm_1d_basic_reflecting.jl
+++ b/examples/bbm_bbm_1d/bbm_bbm_1d_basic_reflecting.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: MattssonNordström2004, derivative_operator
 
diff --git a/examples/bbm_bbm_1d/bbm_bbm_1d_dg.jl b/examples/bbm_bbm_1d/bbm_bbm_1d_dg.jl
index ae57cd1a..e4590b59 100644
--- a/examples/bbm_bbm_1d/bbm_bbm_1d_dg.jl
+++ b/examples/bbm_bbm_1d/bbm_bbm_1d_dg.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using SummationByPartsOperators: legendre_derivative_operator,
                                  UniformPeriodicMesh1D,
                                  couple_discontinuously
diff --git a/examples/bbm_bbm_1d/bbm_bbm_1d_dingemans.jl b/examples/bbm_bbm_1d/bbm_bbm_1d_dingemans.jl
index d79881b2..f19f27d2 100644
--- a/examples/bbm_bbm_1d/bbm_bbm_1d_dingemans.jl
+++ b/examples/bbm_bbm_1d/bbm_bbm_1d_dingemans.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/bbm_bbm_1d/bbm_bbm_1d_fourier.jl b/examples/bbm_bbm_1d/bbm_bbm_1d_fourier.jl
index 4fc9510e..c1b0c17f 100644
--- a/examples/bbm_bbm_1d/bbm_bbm_1d_fourier.jl
+++ b/examples/bbm_bbm_1d/bbm_bbm_1d_fourier.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: fourier_derivative_operator
 
diff --git a/examples/bbm_bbm_1d/bbm_bbm_1d_manufactured.jl b/examples/bbm_bbm_1d/bbm_bbm_1d_manufactured.jl
index 8a9c1006..a28bce1a 100644
--- a/examples/bbm_bbm_1d/bbm_bbm_1d_manufactured.jl
+++ b/examples/bbm_bbm_1d/bbm_bbm_1d_manufactured.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/bbm_bbm_1d/bbm_bbm_1d_relaxation.jl b/examples/bbm_bbm_1d/bbm_bbm_1d_relaxation.jl
index 3524d4f7..54479064 100644
--- a/examples/bbm_bbm_1d/bbm_bbm_1d_relaxation.jl
+++ b/examples/bbm_bbm_1d/bbm_bbm_1d_relaxation.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/bbm_bbm_1d/bbm_bbm_1d_upwind_relaxation.jl b/examples/bbm_bbm_1d/bbm_bbm_1d_upwind_relaxation.jl
index c3a315fb..3365617a 100644
--- a/examples/bbm_bbm_1d/bbm_bbm_1d_upwind_relaxation.jl
+++ b/examples/bbm_bbm_1d/bbm_bbm_1d_upwind_relaxation.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: upwind_operators, periodic_derivative_operator
 using SparseArrays: sparse
diff --git a/examples/bbm_bbm_1d/bbm_bbm_1d_well_balanced.jl b/examples/bbm_bbm_1d/bbm_bbm_1d_well_balanced.jl
index 229a1ce1..9c3eb959 100644
--- a/examples/bbm_bbm_1d/bbm_bbm_1d_well_balanced.jl
+++ b/examples/bbm_bbm_1d/bbm_bbm_1d_well_balanced.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: periodic_derivative_operator
 using SparseArrays: sparse
diff --git a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_conservation.jl b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_conservation.jl
index 23b03894..75c57f0c 100644
--- a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_conservation.jl
+++ b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_conservation.jl
@@ -6,7 +6,7 @@
 #   equations in standard and hyperbolic form
 #   [arXiv: 2408.02665](https://arxiv.org/abs/2408.02665)
 
-using OrdinaryDiffEq
+using OrdinaryDiffEqLowStorageRK
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_dingemans.jl b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_dingemans.jl
index b2eb6f39..012487e9 100644
--- a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_dingemans.jl
+++ b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_dingemans.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqLowStorageRK
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_manufactured.jl b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_manufactured.jl
index 3f8fc64d..b3107bee 100644
--- a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_manufactured.jl
+++ b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_manufactured.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_soliton.jl b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_soliton.jl
index 2b6e6969..9906f407 100644
--- a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_soliton.jl
+++ b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_soliton.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqLowStorageRK
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_soliton_relaxation.jl b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_soliton_relaxation.jl
index 4166639e..ccf84265 100644
--- a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_soliton_relaxation.jl
+++ b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_soliton_relaxation.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqLowStorageRK
 using DispersiveShallowWater
 using SummationByPartsOperators: fourier_derivative_operator
 
diff --git a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_well_balanced.jl b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_well_balanced.jl
index 3b9fad0d..35663746 100644
--- a/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_well_balanced.jl
+++ b/examples/hyperbolic_serre_green_naghdi_1d/hyperbolic_serre_green_naghdi_well_balanced.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqLowStorageRK
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/serre_green_naghdi_1d/serre_green_naghdi_conservation.jl b/examples/serre_green_naghdi_1d/serre_green_naghdi_conservation.jl
index cf1b248d..9f8ee990 100644
--- a/examples/serre_green_naghdi_1d/serre_green_naghdi_conservation.jl
+++ b/examples/serre_green_naghdi_1d/serre_green_naghdi_conservation.jl
@@ -6,7 +6,7 @@
 #   equations in standard and hyperbolic form
 #   [arXiv: 2408.02665](https://arxiv.org/abs/2408.02665)
 
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/serre_green_naghdi_1d/serre_green_naghdi_dingemans.jl b/examples/serre_green_naghdi_1d/serre_green_naghdi_dingemans.jl
index 685ba626..b8592cfd 100644
--- a/examples/serre_green_naghdi_1d/serre_green_naghdi_dingemans.jl
+++ b/examples/serre_green_naghdi_1d/serre_green_naghdi_dingemans.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: upwind_operators, periodic_derivative_operator
 
diff --git a/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton.jl b/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton.jl
index 31c2186e..1eb416a3 100644
--- a/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton.jl
+++ b/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_fourier.jl b/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_fourier.jl
index 6aee789b..a1d1db24 100644
--- a/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_fourier.jl
+++ b/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_fourier.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: fourier_derivative_operator
 
diff --git a/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_relaxation.jl b/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_relaxation.jl
index acfcc4ad..0ed0d420 100644
--- a/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_relaxation.jl
+++ b/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_relaxation.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: fourier_derivative_operator
 
diff --git a/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_upwind.jl b/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_upwind.jl
index 37850ac0..227921ad 100644
--- a/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_upwind.jl
+++ b/examples/serre_green_naghdi_1d/serre_green_naghdi_soliton_upwind.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: upwind_operators, periodic_derivative_operator
 using SparseArrays: sparse
diff --git a/examples/serre_green_naghdi_1d/serre_green_naghdi_well_balanced.jl b/examples/serre_green_naghdi_1d/serre_green_naghdi_well_balanced.jl
index 6cbadda6..023456ff 100644
--- a/examples/serre_green_naghdi_1d/serre_green_naghdi_well_balanced.jl
+++ b/examples/serre_green_naghdi_1d/serre_green_naghdi_well_balanced.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: upwind_operators, periodic_derivative_operator
 
diff --git a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans.jl b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans.jl
index f1d1b618..32a17bf8 100644
--- a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans.jl
+++ b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_cg.jl b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_cg.jl
index cc75b757..422741e7 100644
--- a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_cg.jl
+++ b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_cg.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: legendre_derivative_operator, UniformPeriodicMesh1D,
                                  couple_continuously, legendre_second_derivative_operator
diff --git a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_fourier.jl b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_fourier.jl
index b5fc969e..d61d1e44 100644
--- a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_fourier.jl
+++ b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_fourier.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: fourier_derivative_operator
 
diff --git a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_relaxation.jl b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_relaxation.jl
index aa5b2442..eebbae51 100644
--- a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_relaxation.jl
+++ b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_relaxation.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_upwind.jl b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_upwind.jl
index f57eff3b..10144c2e 100644
--- a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_upwind.jl
+++ b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_upwind.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 using SummationByPartsOperators: upwind_operators, periodic_derivative_operator
 
diff --git a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_manufactured.jl b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_manufactured.jl
index dde4f83f..ef57de85 100644
--- a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_manufactured.jl
+++ b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_manufactured.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_well_balanced.jl b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_well_balanced.jl
index 906bfaff..708ab790 100644
--- a/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_well_balanced.jl
+++ b/examples/svaerd_kalisch_1d/svaerd_kalisch_1d_well_balanced.jl
@@ -1,4 +1,4 @@
-using OrdinaryDiffEq
+using OrdinaryDiffEqTsit5
 using DispersiveShallowWater
 
 ###############################################################################
diff --git a/test/Project.toml b/test/Project.toml
index b9bd8fc1..e42d3fec 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,7 +1,8 @@
 [deps]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 ExplicitImports = "7d51a73a-1435-4ff3-83d9-f097790105c7"
-OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+OrdinaryDiffEqLowStorageRK = "b0944070-b475-4768-8dec-fb6eb410534d"
+OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SummationByPartsOperators = "9f78cca6-572e-554e-b819-917d2f1cf240"
@@ -12,7 +13,8 @@ TestItems = "1c621080-faea-4a02-84b6-bbd5e436b8fe"
 [compat]
 Aqua = "0.7, 0.8"
 ExplicitImports = "1.0.1"
-OrdinaryDiffEq = "6.62"
+OrdinaryDiffEqLowStorageRK = "1.1"
+OrdinaryDiffEqTsit5 = "1.1"
 Plots = "1.25"
 SparseArrays = "1"
 SummationByPartsOperators = "0.5.63"
diff --git a/test/runtests.jl b/test/runtests.jl
index 99ffa9a1..08439f16 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -19,5 +19,5 @@ end
                                      Mattsson2017
 
     using SparseArrays: sparse, SparseMatrixCSC
-    using OrdinaryDiffEq: solve
+    using OrdinaryDiffEqTsit5: solve
 end
diff --git a/test/test_serre_green_naghdi_1d.jl b/test/test_serre_green_naghdi_1d.jl
index 05b9950d..1901b5c6 100644
--- a/test/test_serre_green_naghdi_1d.jl
+++ b/test/test_serre_green_naghdi_1d.jl
@@ -12,7 +12,7 @@ end
                         change_waterheight=0.0,
                         change_entropy_modified=-3.1093350116861984e-11)
 
-    @test_allocations(semi, sol, allocs=550_000)
+    @test_allocations(semi, sol, allocs=650_000)
 end
 
 @testitem "serre_green_naghdi_soliton.jl with bathymetry_mild_slope" setup=[
@@ -110,7 +110,7 @@ end
                         change_waterheight=4.263256414560601e-14,
                         change_entropy_modified=-3.1036506698001176e-11)
 
-    @test_allocations(semi, sol, allocs=500_000)
+    @test_allocations(semi, sol, allocs=600_000)
 end
 
 @testitem "serre_green_naghdi_soliton_upwind.jl with bathymetry_mild_slope" setup=[