Added ARK3 method

Author: brownbaerchen

pySDC/implementations/sweeper_classes/Runge_Kutta.py

@@ -761,8 +761,26 @@ def get_update_order(cls):
 
 
 class ARK2(RungeKuttaIMEX):
+    """
+    Second order two stage singly diagonally implicit globally stiffly accurate IMEX RK method with explicit first stage.
+    Can be used to integrate simple DAEs because explicit and implicit part are both stiffly accurate.
+    """
+
     generator_IMP = RK_SCHEMES["ARK222EDIRK"]()
     generator_EXP = RK_SCHEMES["ARK222ERK"]()
 
     nodes, weights, matrix = generator_IMP.genCoeffs()
     _, weights_explicit, matrix_explicit = generator_EXP.genCoeffs()
+
+
+class ARK3(RungeKuttaIMEX):
+    """
+    Third order four stage singly diagonally implicit globally stiffly accurate IMEX RK method with explicit first stage.
+    Can be used to integrate simple DAEs because explicit and implicit part are both stiffly accurate.
+    """
+
+    generator_IMP = RK_SCHEMES["ARK443ESDIRK"]()
+    generator_EXP = RK_SCHEMES["ARK443ERK"]()
+
+    nodes, weights, matrix = generator_IMP.genCoeffs()
+    _, weights_explicit, matrix_explicit = generator_EXP.genCoeffs()

pySDC/tests/test_sweepers/test_Runge_Kutta_sweeper.py

@@ -27,6 +27,7 @@
     'IMEXEuler',
     'ARK32',
     'ARK2',
+    'ARK3',
 ]
 
 
@@ -168,6 +169,7 @@ def test_order(sweeper_name, useGPU=False):
         'ARK548L2SA': 6,
         'IMEXEuler': 2,
         'ARK2': 3,
+        'ARK3': 4,
         'ARK32': 4,
         'ARK324L2SAERK': 4,
         'ARK324L2SAESDIRK': 4,