jacobwilliams · jacobwilliams · Apr 27, 2025 · Apr 27, 2025 · Apr 27, 2025 · Apr 27, 2025
diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
@@ -10,8 +10,8 @@ jobs:
       fail-fast: false
       matrix:
         os: [ubuntu-latest]
-        gcc_v: [10] # Version of GFortran we want to use.
-        python-version: [3.9]
+        gcc_v: [14] # Version of GFortran we want to use.
+        python-version: [3.12]
     env:
       FC: gfortran-${{ matrix.gcc_v }}
       GCC_V: ${{ matrix.gcc_v }}
@@ -31,7 +31,7 @@ jobs:
       uses: ts-graphviz/setup-graphviz@v1
 
     - name: Setup Fortran Package Manager
-      uses: fortran-lang/setup-fpm@v5
+      uses: fortran-lang/setup-fpm@v7
       with:
         github-token: ${{ secrets.GITHUB_TOKEN }}
 

diff --git a/README.md b/README.md
@@ -24,9 +24,9 @@ The focus of this library is single-step, explicit Runge-Kutta solvers for 1st o
 
 ### Available Runge-Kutta methods:
 
-  * Number of fixed-step methods:    27
+  * Number of fixed-step methods:    28
   * Number of variable-step methods: 48
-  * Total number of methods:         75
+  * Total number of methods:         76
 
 ### Fixed-step methods:
 
@@ -56,6 +56,7 @@ Name       | Description| Properties | Order | Stages   | Registers | CFL  | Ref
 `rk8_10` | 10-stage, 8th order Runge-Kutta Shanks |  | 8 | 10 | 10 |  | [Shanks (1965)](http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19650022581.pdf)
 `rkcv8` | 11-stage, 8th order Runge-Kutta Cooper-Verner |  | 8 | 11 | 11 |  | [Cooper & Verner (1972)](https://epubs.siam.org/doi/abs/10.1137/0709037)
 `rk8_12` | 12-stage, 8th order Runge-Kutta Shanks |  | 8 | 12 | 12 |  | [Shanks (1965)](http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19650022581.pdf)
+`rks10` | 10th order Runge-Kutta Stepanov |  | 10 | 15 | 15 |  | [Stepanov (2025)](https://arxiv.org/abs/2504.17329)
 `rkz10` | 10th order Runge-Kutta Zhang |  | 10 | 16 | 16 |  | [Zhang (2019)](https://arxiv.org/abs/1911.00318)
 `rko10` | 10th order Runge-Kutta Ono |  | 10 | 17 | 17 |  | [Ono (2003)](http://www.peterstone.name/Maplepgs/Maple/nmthds/RKcoeff/Runge_Kutta_schemes/RK10/RKcoeff10f_1.pdf)
 `rkh10` | 10th order Runge-Kutta Hairer |  | 10 | 17 | 17 |  | [Hairer (1978)](https://www.researchgate.net/publication/31221486_A_Runge-Kutta_Method_of_Order_10)
@@ -182,7 +183,9 @@ xf = -0.1360372426E+01  0.1325538438E+01
 
 ### Example performance comparison
 
-Running the unit tests will generate some performance plots. The following is for the variable-step methods compiled with quadruple precision (e.g, `fpm test rk_test_variable_step --compiler ifort --flag "-DREAL128"`): [rk_test_variable_step_R16.pdf](media/rk_test_variable_step_R16.pdf)
+Running the unit tests will generate some performance plots. The following is for the variable-step methods compiled with quadruple precision (e.g, `fpm test rk_test_variable_step --compiler ifort --flag "-DREAL128"`):
+
+![rk_test_variable_step_R16](media/rk_test_variable_step_R16.pdf)
 
 ### Compiling
 

diff --git a/scripts/generate_files.py b/scripts/generate_files.py
@@ -34,6 +34,7 @@
                  ('rk8_10'   , '10-stage, 8th order Runge-Kutta Shanks'                       , '     ', 8     , 10       , 10        , None , '[Shanks (1965)](http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19650022581.pdf)'),
                  ('rkcv8'    , '11-stage, 8th order Runge-Kutta Cooper-Verner'                , '     ', 8     , 11       , 11        , None , '[Cooper & Verner (1972)](https://epubs.siam.org/doi/abs/10.1137/0709037)'),
                  ('rk8_12'   , '12-stage, 8th order Runge-Kutta Shanks'                       , '     ', 8     , 12       , 12        , None , '[Shanks (1965)](http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19650022581.pdf)'),
+                 ('rks10'  , '10th order Runge-Kutta Stepanov'                              , '     ', 10    , 15       , 15        , None , '[Stepanov (2025)](https://arxiv.org/abs/2504.17329)'),
                  ('rkz10'    , '10th order Runge-Kutta Zhang'                                 , '     ', 10    , 16       , 16        , None , '[Zhang (2019)](https://arxiv.org/abs/1911.00318)'),
                  ('rko10'    , '10th order Runge-Kutta Ono'                                   , '     ', 10    , 17       , 17        , None , '[Ono (2003)](http://www.peterstone.name/Maplepgs/Maple/nmthds/RKcoeff/Runge_Kutta_schemes/RK10/RKcoeff10f_1.pdf)'),
                  ('rkh10'    , '10th order Runge-Kutta Hairer'                                , '     ', 10    , 17       , 17        , None , '[Hairer (1978)](https://www.researchgate.net/publication/31221486_A_Runge-Kutta_Method_of_Order_10)')]
@@ -105,8 +106,6 @@ def readme_template():
 
 ### Description
 
-**This is a work in progress!**
-
 The focus of this library is single-step, explicit Runge-Kutta solvers for 1st order differential equations.
 
 ### Novel features:
@@ -153,7 +152,7 @@ def readme_template():
 
 Running the unit tests will generate some performance plots. The following is for the variable-step methods compiled with quadruple precision (e.g, `fpm test rk_test_variable_step --compiler ifort --flag "-DREAL128"`):
 
-![rk_test_variable_step_R16](media/rk_test_variable_step_R16.png)
+![rk_test_variable_step_R16](media/rk_test_variable_step_R16.pdf)
 
 ### Compiling
 

diff --git a/src/rklib_fixed_classes.inc b/src/rklib_fixed_classes.inc
@@ -168,6 +168,13 @@
         procedure :: properties => rk8_12_properties
     end type rk8_12_class
 
+    type,extends(rk_fixed_step_class),public :: rks10_class
+        !! 10th order Runge-Kutta Stepanov
+        contains
+        procedure :: step => rks10
+        procedure :: properties => rks10_properties
+    end type rks10_class
+
     type,extends(rk_fixed_step_class),public :: rkz10_class
         !! 10th order Runge-Kutta Zhang
         contains

diff --git a/src/rklib_fixed_properties.f90 b/src/rklib_fixed_properties.f90
@@ -238,6 +238,15 @@
         p%number_of_registers = 12
     end procedure rk8_12_properties
 
+    module procedure rks10_properties
+        !! Returns the properties of the [[rks10]] method
+        p%short_name = 'rks10'
+        p%long_name = '10th order Runge-Kutta Stepanov'
+        p%order = 10
+        p%number_of_stages = 15
+        p%number_of_registers = 15
+    end procedure rks10_properties
+
     module procedure rkz10_properties
         !! Returns the properties of the [[rkz10]] method
         p%short_name = 'rkz10'

diff --git a/src/rklib_fixed_property_interfaces.inc b/src/rklib_fixed_property_interfaces.inc
@@ -142,6 +142,12 @@ pure module function rk8_12_properties(me) result(p)
     type(rklib_properties) :: p !! properties of the method
 end function rk8_12_properties
 
+pure module function rks10_properties(me) result(p)
+    implicit none
+    class(rks10_class),intent(in) :: me
+    type(rklib_properties) :: p !! properties of the method
+end function rks10_properties
+
 pure module function rkz10_properties(me) result(p)
     implicit none
     class(rkz10_class),intent(in) :: me

diff --git a/src/rklib_fixed_step_interfaces.inc b/src/rklib_fixed_step_interfaces.inc
@@ -216,6 +216,15 @@
         real(wp),dimension(me%n),intent(out) :: xf !! state at time `t+h`
     end subroutine rk8_12
 
+    module subroutine rks10(me,t,x,h,xf)
+        implicit none
+        class(rks10_class),intent(inout) :: me
+        real(wp),intent(in) :: t !! initial time
+        real(wp),dimension(me%n),intent(in) :: x !! initial state
+        real(wp),intent(in) :: h !! time step
+        real(wp),dimension(me%n),intent(out) :: xf !! state at time `t+h`
+    end subroutine rks10
+
     module subroutine rkz10(me,t,x,h,xf)
         implicit none
         class(rkz10_class),intent(inout) :: me