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diff --git a/Project1/Results/V_plus_minus.pdf b/Project1/Results/V_plus_minus.pdf
index 675502b468e12036f7f8be196cca77b2f1a2cff4..2cc33b2b82d4859b3d04790b4ab4018c15c346a3 100644
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diff --git a/Project1/System.py b/Project1/System.py
index e729f76ec0f90610b8c60f02eac00b4332f07b57..0acb271086ce236541c2dd415625603023c8242c 100644
--- a/Project1/System.py
+++ b/Project1/System.py
@@ -206,22 +206,16 @@ class System:
                     n_old[2:] - 2 * n_old[1:-1] + n_old[:-2]
                 )
             )
-            # if type=='Standard':
             n_plus[1:] = n_plus_old[1:] - self.dt * (
                 1 / self.dx  * (upwind_n_plus_1 - upwind_n_plus_2)
             )
-            n_plus[-1] = n_plus[-2]
             n_minus[:-1] = n_minus_old[:-1] - self.dt * (
                 1 /self. dx  * (upwind_n_minus_1 - upwind_n_minus_2)
             )
+
+            # Neumann bcs
+            n_plus[-1] = n_plus[-2]
             n_minus[0] = n_minus[1]
-            # elif type=='Exponential':
-            #     n_plus[1:-1] = n_plus_old[1:-1] - self.dt * (
-            #         1 / self.dx  * (upwind_n_plus_1 - upwind_n_plus_2)
-            #     )
-            #     n_minus[1:-1] = n_minus_old[1:-1] - self.dt * (
-            #         1 / self.dx  * (upwind_n_minus_1 - upwind_n_minus_2)
-            #     )
             
             if exchange == 'None':
                 pass
@@ -234,6 +228,10 @@ class System:
                 n, n_plus, n_minus = self.update_Reaction(n, n_plus, n_minus)
             else:
                 raise ValueError('Exchange method not recognized, must be one of: None, SourceTerms, ReactionTerms, FullTerms')
+            
+            # # Neumann bcs
+            # n_plus[-1] = n_plus[-2]
+            # n_minus[0] = n_minus[1]
 
             # Apply BCs
             n, n_plus, n_minus = self.apply_bcs(n, n_plus, n_minus)
@@ -272,7 +270,7 @@ class System:
         return fig, axs
     
     def plot_analytical_solution(self, t):
-        x, n_init, n_plus_init, n_minus_init = self.Initialization()
+        x, _, _, _ = self.Initialization()
         fig, axs = plt.subplots()
         fig.suptitle(f'Analytical Solution at t={t}')
         axs.plot(x, self.n_plus_ana(x, t), '--o', label='n+')
diff --git a/Project1/Task1_class.ipynb b/Project1/Task1_class.ipynb
index e3fb607914395d6afffc603dfefb779e94e23963..d565a6a6153a044dbc4a8b544806998fce769101 100644
--- a/Project1/Task1_class.ipynb
+++ b/Project1/Task1_class.ipynb
@@ -65,7 +65,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2908415207.py:4: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2908415207.py:4: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -96,7 +96,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/1581121392.py:4: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/1581121392.py:4: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -127,11 +127,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2250181504.py:11: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2250181504.py:11: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2250181504.py:16: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2250181504.py:16: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2250181504.py:21: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2250181504.py:21: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -208,9 +208,9 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/886973050.py:19: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/886973050.py:19: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/886973050.py:24: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/886973050.py:24: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -299,11 +299,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/683968515.py:55: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/683968515.py:55: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/683968515.py:64: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/683968515.py:64: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n",
       "  fig.legend()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/683968515.py:66: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/683968515.py:66: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
       "/Users/janhabscheid/Documents/git/ddm/Project1/System.py:205: RuntimeWarning: overflow encountered in multiply\n",
       "  self.D0 / self.dx**2 * (\n",
@@ -474,7 +474,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/32072315.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/32072315.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -521,7 +521,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2884526579.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2884526579.py:20: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -568,11 +568,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/1435854478.py:17: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/1435854478.py:17: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/1435854478.py:22: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/1435854478.py:22: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/1435854478.py:27: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/1435854478.py:27: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -646,11 +646,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/3019376010.py:21: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/3019376010.py:21: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/3019376010.py:26: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/3019376010.py:26: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/3019376010.py:31: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/3019376010.py:31: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -728,11 +728,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2873779185.py:17: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2873779185.py:17: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2873779185.py:22: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2873779185.py:22: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n",
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2873779185.py:27: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2873779185.py:27: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -856,7 +856,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2597085326.py:33: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2597085326.py:33: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
@@ -916,7 +916,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_92991/2796571549.py:34: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
+      "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_93949/2796571549.py:34: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
       "  fig.show()\n"
      ]
     },
diff --git a/Project1/__pycache__/System.cpython-312.pyc b/Project1/__pycache__/System.cpython-312.pyc
index cf3c1488523de42f832d64c46faad333822bb517..66e2cb352daa7f9ef65c4c81f71b4416057deb9b 100644
Binary files a/Project1/__pycache__/System.cpython-312.pyc and b/Project1/__pycache__/System.cpython-312.pyc differ