TB: added ARK3(2) method (#9)

* Added ARK3(2) method

* Fixed typos

qmat/qcoeff/butcher.py

@@ -775,4 +775,57 @@ class ARK548L2SAERK2(ARK548L2SAESDIRK2):
     A[7, 4] = 4151782504231.0 / 36106512998704.0
     A[7, 5] = 572599549169.0 / 6265429158920.0
     A[7, 6] = -457874356192.0 / 11306498036315.0
-    A[1, 0] = ARK548L2SAESDIRK2.c[1]
+    A[1, 0] = ARK548L2SAESDIRK2.c[1]
+
+
+@registerRK
+class ARK324L2SAERK(RK):
+    """
+    Explicit part of embedded additive Runge-Kutta pair of orders 3 and 2. See https://doi.org/10.1016/S0168-9274(02)00138-1
+    """
+    A = np.zeros((4, 4))
+    A[1, 0] = 1767732205903./2027836641118.
+    A[2, 0] = 5535828885825./10492691773637.
+    A[2, 1] = 788022342437./10882634858940.
+    A[3, 0] = 6485989280629./16251701735622.
+    A[3, 1] = -4246266847089./9704473918619.
+    A[3, 2] = 10755448449292./10357097424841.
+
+    b = np.zeros(4)
+    b[0] = 1471266399579./7840856788654.
+    b[1] = -4482444167858./7529755066697.
+    b[2] = 11266239266428./11593286722821.
+    b[3] = 1767732205903./4055673282236.
+
+    b2 = np.zeros(4)
+    b2[0] = 2756255671327./12835298489170.
+    b2[1] = -10771552573575./22201958757719.
+    b2[2] = 9247589265047./10645013368117.
+    b2[3] = 2193209047091./5459859503100.
+
+    c = np.zeros(4)
+    c[1] = 1767732205903./2027836641118.
+    c[2] = 3./5.
+    c[3] = 1.
+
+    @property
+    def order(self): return 3
+
+
+@registerRK
+class ARK324L2SAESDIRK(ARK324L2SAERK):
+    """
+    Implicit part of embedded additive Runge-Kutta pair of orders 3 and 2. See https://doi.org/10.1016/S0168-9274(02)00138-1
+    """
+    A = np.zeros((4, 4), dtype=float)
+    A[1, 0] = 1767732205903./4055673282236.
+    A[1, 1] = 1767732205903./4055673282236.
+    A[2, 0] = 2746238789719./10658868560708.
+    A[2, 1] = -640167445237./6845629431997.
+    A[2, 2] = 1767732205903./4055673282236.
+    A[3, 0] = 1471266399579./7840856788654.
+    A[3, 1] = -4482444167858./7529755066697.
+    A[3, 2] = 11266239266428./11593286722821.
+    A[3, 3] = 1767732205903./4055673282236.
+
+    CONV_TEST_NSTEPS = [120, 100, 80]