From 6fa426b9aa94115fe4bc7c60791daa9b31879843 Mon Sep 17 00:00:00 2001
From: Thomas Baumann <39156931+brownbaerchen@users.noreply.github.com>
Date: Wed, 6 Nov 2024 12:46:07 +0100
Subject: [PATCH 1/2] Added ARK443 method

---
 qmat/qcoeff/butcher.py | 37 +++++++++++++++++++++++++++++++++++++
 1 file changed, 37 insertions(+)

diff --git a/qmat/qcoeff/butcher.py b/qmat/qcoeff/butcher.py
index 1c59db3..200c563 100644
--- a/qmat/qcoeff/butcher.py
+++ b/qmat/qcoeff/butcher.py
@@ -855,6 +855,7 @@ class ARK222EDIRK(RK):
     @property
     def order(self): return 2
 
+
 @registerRK
 class ARK222ERK(ARK222EDIRK):
     """
@@ -865,3 +866,39 @@ class ARK222ERK(ARK222EDIRK):
                   [ARK222EDIRK.gamma,  0 , 0],
                   [ARK222EDIRK.delta, 1-ARK222EDIRK.delta, 0]])
     b = A[-1, :]
+
+
+@registerRK
+class ARK443ESDIRK(RK):
+    """
+    3rd-order 4-stage ESDIRK scheme [Ascher 1997 sec 2.8]
+    Use as implicit part for ARK scheme in combination with ARK443ERK.
+    """
+
+    c = np.array([0, 1/2, 2/3, 1/2, 1])
+
+    A = np.array([[0,   0 ,   0 ,  0 ,  0 ],
+                  [0,  1/2,   0 ,  0 ,  0 ],
+                  [0,  1/6,  1/2,  0 ,  0 ],
+                  [0, -1/2,  1/2, 1/2,  0 ],
+                  [0,  3/2, -3/2, 1/2, 1/2]])
+
+
+    b = A[-1, :]
+
+    @property
+    def order(self): return 3
+
+
+@registerRK
+class ARK443ERK(ARK443ESDIRK):
+    """
+    3rd-order 4-stage ERK scheme [Ascher 1997 sec 2.8]
+    Use as explicit part for ARK scheme in combination with ARK443EDIRK.
+    """
+    A = np.array([[  0  ,   0  ,  0 ,   0 , 0],
+                  [ 1/2 ,   0  ,  0 ,   0 , 0],
+                  [11/18,  1/18,  0 ,   0 , 0],
+                  [ 5/6 , -5/6 , 1/2,   0 , 0],
+                  [ 1/4 ,  7/4 , 3/4, -7/4, 0]])
+    b = A[-1, :]

From eaf0ce63fc32f1392b88e75bba0ae7c8c16e378f Mon Sep 17 00:00:00 2001
From: Thomas Baumann <39156931+brownbaerchen@users.noreply.github.com>
Date: Wed, 6 Nov 2024 12:49:41 +0100
Subject: [PATCH 2/2] Fixed typo

---
 qmat/qcoeff/butcher.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/qmat/qcoeff/butcher.py b/qmat/qcoeff/butcher.py
index 200c563..ad43bd8 100644
--- a/qmat/qcoeff/butcher.py
+++ b/qmat/qcoeff/butcher.py
@@ -894,7 +894,7 @@ def order(self): return 3
 class ARK443ERK(ARK443ESDIRK):
     """
     3rd-order 4-stage ERK scheme [Ascher 1997 sec 2.8]
-    Use as explicit part for ARK scheme in combination with ARK443EDIRK.
+    Use as explicit part for ARK scheme in combination with ARK443ESDIRK.
     """
     A = np.array([[  0  ,   0  ,  0 ,   0 , 0],
                   [ 1/2 ,   0  ,  0 ,   0 , 0],