From df0b21109ace56aac92f8200e53d5888b049ae2c Mon Sep 17 00:00:00 2001
From: Cody Balos <balos1@llnl.gov>
Date: Fri, 20 Oct 2023 14:03:50 -0700
Subject: [PATCH 1/2] Bugfix: docs missing cvodequadsstolerances (#352)

Fix CVodeQuadSStolerances docs, add CVodeQuadSVtolerances docs (Fixes #340)
---
 doc/cvodes/guide/source/Usage/ADJ.rst |  2 +-
 doc/cvodes/guide/source/Usage/SIM.rst | 22 +++++++++++++++++++---
 2 files changed, 20 insertions(+), 4 deletions(-)

diff --git a/doc/cvodes/guide/source/Usage/ADJ.rst b/doc/cvodes/guide/source/Usage/ADJ.rst
index db4d6b9655..80e567f024 100644
--- a/doc/cvodes/guide/source/Usage/ADJ.rst
+++ b/doc/cvodes/guide/source/Usage/ADJ.rst
@@ -24,7 +24,7 @@ several supporting user-callable functions. For this reason, in the following
 sections we refer to the *backward problem* and not to the *adjoint problem*
 when discussing details relevant to the ODEs that are integrated backward in
 time. The backward problem can be the adjoint problem :eq:`CVODES_adj_eqns` or
-:eq:`CVODES_adj_eqns`, and can be augmented with some quadrature differential
+:eq:`CVODES_adj1_eqns`, and can be augmented with some quadrature differential
 equations.
 
 CVODES uses various constants for both input and output. These are defined as
diff --git a/doc/cvodes/guide/source/Usage/SIM.rst b/doc/cvodes/guide/source/Usage/SIM.rst
index dbc6506dd1..539f521ea7 100644
--- a/doc/cvodes/guide/source/Usage/SIM.rst
+++ b/doc/cvodes/guide/source/Usage/SIM.rst
@@ -4122,13 +4122,13 @@ If the quadrature variables are part of the step size control mechanism,
 one of the following functions must be called to specify the
 integration tolerances for quadrature variables.
 
-.. c:function:: int CVodeQuadSVtolerances(void * cvode_mem, realtype reltolQ, N_Vector abstolQ)
+.. c:function:: int CVodeQuadSStolerances(void *cvode_mem, realtype reltolQ, realtype abstolQ)
 
-   The function ``CVodeQuadSStolerances`` specifies scalar relative and absolute  tolerances.
+   The function ``CVodeQuadSStolerances`` specifies scalar relative and absolute tolerances.
 
    **Arguments:**
      * ``cvode_mem`` -- pointer to the CVODES memory block.
-     * ``reltolQ`` --  tolerances is the scalar relative error tolerance.
+     * ``reltolQ`` --  is the scalar relative error tolerance.
      * ``abstolQ`` -- is the scalar absolute error tolerance.
 
    **Return value:**
@@ -4138,6 +4138,22 @@ integration tolerances for quadrature variables.
      * ``CV_ILL_INPUT`` -- One of the input tolerances was negative.
 
 
+.. c:function:: int CVodeQuadSVtolerances(void * cvode_mem, realtype reltolQ, N_Vector abstolQ)
+
+   The function ``CVodeQuadSVtolerances`` specifies scalar relative and vector absolute tolerances.
+
+   **Arguments:**
+     * ``cvode_mem`` -- pointer to the CVODES memory block.
+     * ``reltolQ`` --  is the scalar relative error tolerance.
+     * ``abstolQ`` -- the vector of absolute error tolerances.
+
+   **Return value:**
+     * ``CV_SUCCESS`` -- The optional value has been successfully set.
+     * ``CV_NO_QUAD`` -- Quadrature integration was not initialized.
+     * ``CV_MEM_NULL`` -- The ``cvode_mem`` pointer is ``NULL``.
+     * ``CV_ILL_INPUT`` -- One of the input tolerances was negative.
+
+
 .. _CVODES.Usage.purequad.optional_output:
 
 Optional outputs for quadrature integration

From 6ae281ef1a6c366fc3ed91322c1626907a5507a0 Mon Sep 17 00:00:00 2001
From: Steven Roberts <roberts115@llnl.gov>
Date: Thu, 26 Oct 2023 07:18:42 -0700
Subject: [PATCH 2/2] Add Sofroniou-Spaletta-5-3-4 method only (#355)

Only adding the `Sofroniou-Spaletta-5-3-4` method but not changing the
defaults like #345

---------

Co-authored-by: Daniel R. Reynolds <reynolds@smu.edu>
Co-authored-by: David Gardner <gardner48@llnl.gov>
---
 CHANGELOG.md                                  |   2 +
 doc/arkode/guide/source/Butcher.rst           |  37 ++++++++++++++++++
 doc/arkode/guide/source/Constants.rst         |   2 +
 doc/arkode/guide/source/Introduction.rst      |   2 +
 .../sofroniou_spaletta_erk_stab_region.png    | Bin 0 -> 25026 bytes
 doc/shared/sundials.bib                       |  12 ++++++
 include/arkode/arkode_butcher_erk.h           |   3 +-
 src/arkode/arkode_butcher_erk.def             |  34 ++++++++++++++++
 8 files changed, 91 insertions(+), 1 deletion(-)
 create mode 100644 doc/shared/figs/arkode/sofroniou_spaletta_erk_stab_region.png

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4182e059f3..4b1c49a4a2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -27,6 +27,8 @@ Fixed scaling bug in `SUNMatScaleAddI_Sparse` for non-square matrices.
 Fixed missing soversions in some `SUNLinearSolver` and `SUNNonlinearSolver`
 CMake targets.
 
+Added the fourth order ERK method `ARKODE_SOFRONIOU_SPALETTA_5_3_4`.
+
 ## Changes to SUNDIALS in release 6.6.1
 
 Updated the Tpetra NVector interface to support Trilinos 14.
diff --git a/doc/arkode/guide/source/Butcher.rst b/doc/arkode/guide/source/Butcher.rst
index ecafdab263..c9166aa55a 100644
--- a/doc/arkode/guide/source/Butcher.rst
+++ b/doc/arkode/guide/source/Butcher.rst
@@ -331,6 +331,43 @@ This is the default 3th order slow and fast MRIStep method (from
    Linear stability region for the Knoth-Wolke method
 
 
+.. _Butcher.Sofroniou_Spaletta:
+
+Sofroniou-Spaletta-5-3-4
+^^^^^^^^^^^^^^^^^^^^^^^^
+
+.. index:: Sofroniou-Spaletta-5-3-4 ERK method
+
+Accessible via the constant ``ARKODE_SOFRONIOU_SPALETTA_5_3_4`` to
+:c:func:`ARKStepSetTableNum`, :c:func:`ERKStepSetTableNum`
+or :c:func:`ARKodeButcherTable_LoadERK`.
+Accessible via the string ``"ARKODE_SOFRONIOU_SPALETTA_5_3_4"`` to
+:c:func:`ARKStepSetTableName`, :c:func:`ERKStepSetTableName` or
+:c:func:`ARKodeButcherTable_LoadERKByName`.
+(from :cite:p:`Sof:04`).
+
+.. math::
+
+   \renewcommand{\arraystretch}{1.5}
+   \begin{array}{r|ccccc}
+     0 & 0 & 0 & 0 & 0 & 0 \\
+     \frac{2}{5} & \frac{2}{5} & 0 & 0 & 0 & 0 \\
+     \frac{3}{5} & -\frac{3}{20} & \frac{3}{4} & 0 & 0 & 0 \\
+     1 & \frac{19}{44} & -\frac{15}{44} & \frac{10}{11} & 0 & 0 \\
+     1 & \frac{11}{72} & \frac{25}{72} & \frac{25}{72} & \frac{11}{72} & 0 \\
+     4 & \frac{11}{72} & \frac{25}{72} & \frac{25}{72} & \frac{11}{72} & 0 \\
+     3 & \frac{1251515}{8970912} & \frac{3710105}{8970912} & \frac{2519695}{8970912} & \frac{61105}{8970912} & \frac{119041}{747576} \\
+   \end{array}
+
+.. figure:: /figs/arkode/sofroniou_spaletta_erk_stab_region.png
+   :scale: 50 %
+   :align: center
+
+   Linear stability region for the Sofroniou-Spaletta method.  The method's
+   region is outlined in blue; the embedding's region is in red.
+
+
+
 
 .. _Butcher.Zonneveld:
 
diff --git a/doc/arkode/guide/source/Constants.rst b/doc/arkode/guide/source/Constants.rst
index 9a3e6600ac..95b6a43125 100644
--- a/doc/arkode/guide/source/Constants.rst
+++ b/doc/arkode/guide/source/Constants.rst
@@ -80,6 +80,8 @@ contains the ARKODE output constants.
    +-----------------------------------------------+------------------------------------------------------------+
    | :index:`ARKODE_ARK324L2SA_ERK_4_2_3`          | Use the ARK-4-2-3 ERK method.                              |
    +-----------------------------------------------+------------------------------------------------------------+
+   | :index:`ARKODE_SOFRONIOU_SPALETTA_5_3_4`      | Use the Sofroniou-Spaletta-5-3-4 ERK method.               |
+   +-----------------------------------------------+------------------------------------------------------------+
    | :index:`ARKODE_ZONNEVELD_5_3_4`               | Use the Zonneveld-5-3-4 ERK method.                        |
    +-----------------------------------------------+------------------------------------------------------------+
    | :index:`ARKODE_ARK436L2SA_ERK_6_3_4`          | Use the ARK-6-3-4 ERK method.                              |
diff --git a/doc/arkode/guide/source/Introduction.rst b/doc/arkode/guide/source/Introduction.rst
index 3b5d5ac711..4fafa4d0bb 100644
--- a/doc/arkode/guide/source/Introduction.rst
+++ b/doc/arkode/guide/source/Introduction.rst
@@ -153,6 +153,8 @@ Fixed scaling bug in ``SUNMatScaleAddI_Sparse`` for non-square matrices.
 Fixed missing soversions in some ``SUNLinearSolver`` and ``SUNNonlinearSolver``
 CMake targets.
 
+Added the fourth order ERK method ``ARKODE_SOFRONIOU_SPALETTA_5_3_4``.
+
 Changes in v5.6.1
 -----------------
 
diff --git a/doc/shared/figs/arkode/sofroniou_spaletta_erk_stab_region.png b/doc/shared/figs/arkode/sofroniou_spaletta_erk_stab_region.png
new file mode 100644
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literal 0
HcmV?d00001

diff --git a/doc/shared/sundials.bib b/doc/shared/sundials.bib
index 7972a7b814..af8882cc04 100644
--- a/doc/shared/sundials.bib
+++ b/doc/shared/sundials.bib
@@ -2053,6 +2053,18 @@ @article{Sof:02
   pages   = {506--515}
 }
 
+@article{Sof:04,
+  author = {M. Sofroniou and G. Spaletta},
+  title = {Construction of explicit {Runge-Kutta} pairs with stiffness detection},
+  journal = {Mathematical and Computer Modelling},
+  volume = {40},
+  number = {11},
+  pages = {1157-1169},
+  year = {2004},
+  issn = {0895-7177},
+  doi = {10.1016/j.mcm.2005.01.010}
+}
+
 @article{Ver:78,
   author  = {Verner, J.H},
   title   = {Explicit Runge-Kutta methods with estimates of the local truncation error},
diff --git a/include/arkode/arkode_butcher_erk.h b/include/arkode/arkode_butcher_erk.h
index 6673acb119..1fa298ae75 100644
--- a/include/arkode/arkode_butcher_erk.h
+++ b/include/arkode/arkode_butcher_erk.h
@@ -85,7 +85,8 @@ typedef enum {
   ARKODE_ARK437L2SA_ERK_7_3_4,
   ARKODE_ARK548L2SAb_ERK_8_4_5,
   ARKODE_ARK2_ERK_3_1_2,
-  ARKODE_MAX_ERK_NUM = ARKODE_ARK2_ERK_3_1_2
+  ARKODE_SOFRONIOU_SPALETTA_5_3_4,
+  ARKODE_MAX_ERK_NUM = ARKODE_SOFRONIOU_SPALETTA_5_3_4
 } ARKODE_ERKTableID;
 
 /* Accessor routine to load built-in ERK table */
diff --git a/src/arkode/arkode_butcher_erk.def b/src/arkode/arkode_butcher_erk.def
index f25fafb830..5cfb3f2af6 100644
--- a/src/arkode/arkode_butcher_erk.def
+++ b/src/arkode/arkode_butcher_erk.def
@@ -41,6 +41,7 @@
      ARKODE_HEUN_EULER_2_1_2             Y
      ARKODE_BOGACKI_SHAMPINE_4_2_3       Y
      ARKODE_ARK324L2SA_ERK_4_2_3*        N
+     ARKODE_SOFRONIOU_SPALETTA_5_3_4     Y
      ARKODE_ZONNEVELD_5_3_4              Y
      ARKODE_ARK436L2SA_ERK_6_3_4*        N
      ARKODE_ARK437L2SA_ERK_7_3_4*        N
@@ -165,6 +166,39 @@ ARK_BUTCHER_TABLE(ARKODE_ARK324L2SA_ERK_4_2_3, { /* ARK3(2)4L[2]SA-ERK */
     return B;
   })
 
+ARK_BUTCHER_TABLE(ARKODE_SOFRONIOU_SPALETTA_5_3_4, { /* Sofroniou-Spaletta-ERK */
+    ARKodeButcherTable B = ARKodeButcherTable_Alloc(5, SUNTRUE);
+    B->q = 4;
+    B->p = 3;
+    B->A[1][0] = RCONST(2.0) / RCONST(5.0);
+    B->A[2][0] = RCONST(-3.0) / RCONST(20.0);
+    B->A[2][1] = RCONST(3.0) / RCONST(4.0);
+    B->A[3][0] = RCONST(19.0)/RCONST(44.0);
+    B->A[3][1] = RCONST(-15.0)/RCONST(44.0);
+    B->A[3][2] = RCONST(10.0)/RCONST(11.0);
+    B->A[4][0] = RCONST(11.0)/RCONST(72.0);
+    B->A[4][1] = RCONST(25.0)/RCONST(72.0);
+    B->A[4][2] = RCONST(25.0)/RCONST(72.0);
+    B->A[4][3] = RCONST(11.0)/RCONST(72.0);
+
+    B->b[0] = RCONST(11.0)/RCONST(72.0);
+    B->b[1] = RCONST(25.0)/RCONST(72.0);
+    B->b[2] = RCONST(25.0)/RCONST(72.0);
+    B->b[3] = RCONST(11.0)/RCONST(72.0);
+
+    B->d[0] = RCONST(1251515.0)/RCONST(8970912.0);
+    B->d[1] = RCONST(3710105.0)/RCONST(8970912.0);
+    B->d[2] = RCONST(2519695.0)/RCONST(8970912.0);
+    B->d[3] = RCONST(61105.0)/RCONST(8970912.0);
+    B->d[4] = RCONST(119041.0)/RCONST(747576.0);
+
+    B->c[1] = RCONST(2.0) / RCONST(5.0);
+    B->c[2] = RCONST(3.0) / RCONST(5.0);
+    B->c[3] = RCONST(1.0);
+    B->c[4] = RCONST(1.0);
+    return B;
+  })
+
 ARK_BUTCHER_TABLE(ARKODE_ZONNEVELD_5_3_4, { /* Zonneveld */
     ARKodeButcherTable B = ARKodeButcherTable_Alloc(5, SUNTRUE);
     B->q = 4;