TL: more mathjax fixes

Author: tlunet

docs/notebooks/12_nonLinearRK.ipynb

@@ -63,11 +63,11 @@
     "Consider for example the perturbed Lorenz attractor :\n",
     "\n",
     "$$\n",
-    "\\begin{align}\n",
+    "\\begin{aligned}\n",
     "\\frac{dx}{dt} &= \\sigma(y-x) \\\\\n",
     "\\frac{dy}{dy} &= x(\\rho(t)-z) - y, \\quad \\rho(t) = \\rho_0 + \\epsilon \\sin(t) \\\\\n",
     "\\frac{dz}{dt} &= xy - \\beta z\n",
-    "\\end{align}\n",
+    "\\end{aligned}\n",
     "$$\n",
     "\n",
     "Before solving it, we first need to define its **differential operator** $f(u, t)$ with $u=[x,y,z]^T$\n",

docs/notebooks/14_phiIntegrator.ipynb

@@ -156,23 +156,23 @@
     "Defining $\\Delta{\\tau}_m = t_{m}-t_{m-1}$, we have for each node\n",
     "\n",
     "$$\n",
-    "\\begin{align}\n",
+    "\\begin{aligned}\n",
     "u_1 - \\Delta{\\tau}_1 f(u_1, t_1) &= u_0 \\\\\n",
     "u_2 - \\Delta{\\tau}_2 f(u_2, t_2) &= u_1 \\\\\n",
     "\\dots& \\\\\n",
     "u_M - \\Delta{\\tau}_M f(u_M, t_M) &= u_{M-1}\n",
-    "\\end{align}\n",
+    "\\end{aligned}\n",
     "$$\n",
     "\n",
     "By substitution we can rearrange those into :\n",
     "\n",
     "$$\n",
-    "\\begin{align}\n",
+    "\\begin{aligned}\n",
     "u_1 - \\Delta{\\tau}_1 f(u_1, t_1) &= u_0 \\\\\n",
     "u_2 - \\Delta{\\tau}_2 f(u_2, t_2) - \\Delta{\\tau}_1 f(u_1, t_1) &= u_0 \\\\\n",
     "\\dots& \\\\\n",
     "u_M - \\Delta{\\tau}_M f(u_M, t_M) - \\dots - \\Delta{\\tau}_1 f(u_1, t_1) &= u_0\n",
-    "\\end{align}\n",
+    "\\end{aligned}\n",
     "$$\n",
     "\n",
     "so we can identify the $\\phi$ function for Backward Euler :\n",

qmat/solvers/generic/__init__.py

@@ -444,12 +444,12 @@ def solveSDC(self, nSweeps, Q, weights, QDelta, uNum=None, tInit=0):
 
         .. math::
 
-            \begin{align}
+            \begin{aligned}
             u_{m}^{k+1} - \Delta{t}q^\Delta_{m,m}f(u_m^{k+1},t_m)
                 =&~ u_0 + \Delta{t}\sum_{j=1}^{M}q_{m,j}f(u_j^k, t_j) \\
             &+ \Delta{t}\sum_{j=1}^{m-1}q^\Delta_{m,j}f(u_j^{k+1},t_j)
             - \Delta{t}\sum_{j=1}^{m}q^\Delta_{m,j}f(u_j^{k},t_j),
-            \end{align}
+            \end{aligned}
 
         where :math:`q^\Delta_{i,j}` and :math:`q_{i,j}` are the coefficients
         of :math:`Q_\Delta` and :math:`Q`, respectively.