diff --git a/pySDC/implementations/problem_classes/AllenCahn_MPIFFT.py b/pySDC/implementations/problem_classes/AllenCahn_MPIFFT.py
index 13d3213851..17f770d218 100644
--- a/pySDC/implementations/problem_classes/AllenCahn_MPIFFT.py
+++ b/pySDC/implementations/problem_classes/AllenCahn_MPIFFT.py
@@ -23,14 +23,14 @@ class allencahn_imex(ptype):
     .. math::
         u({\bf x}, 0) = \tanh\left(\frac{r - \sqrt{(x_i-0.5)^2 + (y_j-0.5)^2}}{\sqrt{2}\varepsilon}\right),
 
-    for :math::`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, the problem is treated
+    for :math:`i, j=0,..,N-1`, where :math:`N` is the number of spatial grid points. For time-stepping, the problem is treated
     *semi-implicitly*, i.e., the linear part is solved with Fast-Fourier Tranform (FFT) and the nonlinear part in the right-hand
-    side will be treated explicitly using mpi4py-fft [1]_ to solve them.
+    side will be treated explicitly using ``mpi4py-fft`` [1]_ to solve them.
 
     Parameters
     ----------
     nvars : List of int tuples, optional
-        Number of unknowns in the problem, e.g. [(128, 128), (128, 128)].
+        Number of unknowns in the problem, e.g. ``nvars=(128, 128)``.
     eps : float, optional
         Scaling parameter :math:`\varepsilon`.
     radius : float, optional
@@ -76,12 +76,12 @@ def __init__(
         dw=0.0,
         L=1.0,
         init_type='circle',
-        comm=None,
+        comm=MPI.COMM_WORLD,
     ):
         """Initialization routine"""
 
         if nvars is None:
-            nvars = [(128, 128), (32, 32)]
+            nvars = (128, 128)
 
         if not (isinstance(nvars, tuple) and len(nvars) > 1):
             raise ProblemError('Need at least two dimensions')
diff --git a/pySDC/implementations/problem_classes/generic_ND_FD.py b/pySDC/implementations/problem_classes/generic_ND_FD.py
index 383b244dda..3cb7e6d7cd 100644
--- a/pySDC/implementations/problem_classes/generic_ND_FD.py
+++ b/pySDC/implementations/problem_classes/generic_ND_FD.py
@@ -22,7 +22,7 @@ class GenericNDimFinDiff(ptype):
     .. math::
         \frac{d u}{dt} = A u,
 
-    where :math:`A \in \mathbb{R}^{nN \times nN} is a matrix arising from finite difference discretisation of spatial
+    where :math:`A \in \mathbb{R}^{nN \times nN}` is a matrix arising from finite difference discretisation of spatial
     derivatives with :math:`n` degrees of freedom per dimension and :math:`N` dimensions. This generic class follows the MOL
     (method-of-lines) approach and can be used to discretize partial differential equations such as the advection
     equation and the heat equation.