Add Sheet

sheet/numerical-method/09-10/Numerical-Differentiation-1.ipynb

@@ -138,7 +138,9 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "def f1x(x):\n",
@@ -345,7 +347,9 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "import sympy\n",
@@ -355,7 +359,9 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "x,y,z,e = sympy.Symbol('x'), sympy.Symbol('y'), sympy.Symbol('z'), sympy.Symbol('e')"
@@ -364,7 +370,9 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "from sympy import sin, cos"
@@ -373,7 +381,9 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "y = sin(x)*e**(-cos(x))"
@@ -472,7 +482,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": []
   },
@@ -567,7 +579,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.3"
+   "version": "3.6.1"
   }
  },
  "nbformat": 4,

sheet/numerical-method/09-10/Numerical-Differentiation-2.ipynb

@@ -333,6 +333,27 @@
     "| 0.00125 | 1.28       | 0.367879 |  0.912121 |\n"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.36787944117144233"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from numpy import e\n",
+    "e**(-1)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -371,6 +392,135 @@
     "G = 0.367843\n",
     "$$\n"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.3678361863589256"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def extra(h1,p):\n",
+    "    from math import e\n",
+    "    g1 = (e**(-(1+h1)) - 2*e**(-1) + e**(-(1-h1)))/(h1**2)\n",
+    "    h1=h1/2\n",
+    "    g2 = (e**(-(1+h1)) - 2*e**(-1) + e**(-(1-h1)))/(h1**2)\n",
+    "    return ((2**p)*g2-g1)/((2**p)-1)\n",
+    "extra(0.64,2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.3678361863589256"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def G(h):\n",
+    "    from math import e\n",
+    "    return (e**(-(1+h)) - 2*e**(-1) + e**(-(1-h)))/(h**2)\n",
+    "def extra(h1,p):\n",
+    "    return ((2**p)*G(h1/2)-G(h1))/((2**p)-1)\n",
+    "extra(0.64,2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.36784333333333336"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def extra(g1,g2,p):\n",
+    "    return ((2**p)*g2-g1)/((2**p)-1)\n",
+    "extra(0.380610,0.371035,2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.36784333333333336"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def g(h):\n",
+    "    cda = {\n",
+    "        0.64:0.380610,\n",
+    "        0.32:0.371035,\n",
+    "        0.16:0.368711,\n",
+    "        0.08:0.368281,\n",
+    "        0.04:0.36875,\n",
+    "        0.02:0.37,\n",
+    "        0.01:0.38,\n",
+    "        0.005:0.40,\n",
+    "        0.0025:0.48,\n",
+    "        0.00125:1.28\n",
+    "    }\n",
+    "    return cda[h]\n",
+    "def extra(h,p):\n",
+    "    return ((2**p)*g(h/2)-g(h))/((2**p)-1)\n",
+    "extra(0.64,2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.36784333333333336"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "((2**2)*0.371035-0.380610)/3"
+   ]
   }
  ],
  "metadata": {