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Author: john-s-butler-dit

Chapter 01 - Euler Methods/1_Problem Sheet/102b_Problem_Sheet.ipynb

@@ -33,7 +33,7 @@
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-        "<a href=\"https://colab.research.google.com/github/john-s-butler-dit/Numerical-Analysis-Python/blob/master/Chapter%2001%20-%20Euler%20Methods/1_Problem%20Sheet/01_Problem%20Sheet%201%20Question%202b.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+        "<a href=\"https://colab.research.google.com/github/john-s-butler-dit/Numerical-Analysis-Python/blob/master/Chapter%2001%20-%20Euler%20Methods/1_Problem%20Sheet/102b_Problem_Sheet.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
       ]
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     {
@@ -73,7 +73,7 @@
         "\n",
         "warnings.filterwarnings(\"ignore\")"
       ],
-      "execution_count": 8,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -120,7 +120,7 @@
         "plt.title('Illustration of discrete time points for h=%s'%(h))\n",
         "plt.plot();"
       ],
-      "execution_count": 9,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "display_data",
@@ -167,7 +167,7 @@
         "for i in range (0,N):\n",
         "    w[i+1]=w[i]+h*(w[i]-t[i])"
       ],
-      "execution_count": 10,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -178,7 +178,7 @@
       "source": [
         "y=np.exp(t)+t+1 # Exact Solution"
       ],
-      "execution_count": 11,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -212,7 +212,7 @@
         " \\begin{equation}|y(t_1)-w_1|<\\tau=\\frac{Mh}{2}=\\frac{8h}{2}=4h.\\end{equation}\n",
         "### Lipschitz constant\n",
         "The Lipschitz constant $L$ is from the Lipschitz condition,\n",
-        " \\begin{equation}\\left| \\frac{\\partial f(t,y)}{\\partial t}\\right|\\leq L. \\end{equation}\n",
+        " \\begin{equation}\\left| \\frac{\\partial f(t,y)}{\\partial y}\\right|\\leq L. \\end{equation}\n",
         "The constant can be found by taking partical derivative of $f(t,y)=y-t$ with respect to $y$\n",
         " \\begin{equation}\\frac{\\partial f(t,y)}{\\partial y}=1\\end{equation}\n",
         " \\begin{equation}L=1.\\end{equation}\n",
@@ -230,7 +230,7 @@
       "source": [
         "Upper_bound=8*h/(2*1)*(np.exp(t)-1) # Upper Bound"
       ],
-      "execution_count": 12,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -285,7 +285,7 @@
         "plt.tight_layout()\n",
         "plt.subplots_adjust(top=0.85)    "
       ],
-      "execution_count": 13,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "display_data",
@@ -317,7 +317,7 @@
         "df = pd.DataFrame(data=d)\n",
         "df"
       ],
-      "execution_count": 14,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "execute_result",
@@ -415,7 +415,7 @@
       "source": [
         ""
       ],
-      "execution_count": 14,
+      "execution_count": null,
       "outputs": []
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