Make derivative computation explicit in demo7

PDEs/Demo7_HyperbolicPDEFourier.ipynb

@@ -204,7 +204,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -221,9 +221,11 @@
     "    conditions.\"\"\"\n",
     "\n",
     "    g, Pi, Phi = u[0], u[1], u[2]\n",
-    "    gDot = -Pi\n",
-    "    PiDot = -Fourier.dudx_Fourier(Phi)\n",
-    "    PhiDot = -Fourier.dudx_Fourier(Pi)\n",
+    "    gDot = -Pi    \n",
+    "    # PiDot = -Fourier.dudx_Fourier(Phi)\n",
+    "    # PhiDot = -Fourier.dudx_Fourier(Pi)\n",
+    "    PiDot = -info.D1 @ Phi\n",
+    "    PhiDot = -info.D1 @ Pi\n",
     "\n",
     "    dudt = u.copy() # create data structure of the same shape as `u`\n",
     "    dudt[0] = gDot\n",