Illarionov_855_L6.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Лабораторная работа №6\n",
    "\n",
    "## Вариант 1. Задание 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Условие задачи"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Численно и аналитически решить одну из смешанных задач для квазилинейного уравнения теплопроводности с точностью $\\varepsilon = 10^{-4}$ и сравнить их значения в одиннадцати равноудаленных точках в момент времени $T = 1$\n",
    "\n",
    "$$\n",
    "\\begin{equation*}\n",
    "    \\begin{cases}\n",
    "        \\dfrac{\\partial U}{\\partial t} = \\dfrac{\\partial}{\\partial x} \\left( U \\dfrac{\\partial U}{\\partial x} \\right), \\hspace{0.5cm} 0 < t \\le 1 \\hspace{0.5cm} 0 < x < 1 \\\\\n",
    "        u(0, x) = \\dfrac{(1 + x)^2}{7}, \\hspace{1cm} 0 \\le x \\le 1 \\\\\n",
    "        u(t, 0) = \\dfrac{1}{7 - 6t} \\hspace{1cm} u(t, 1) = \\dfrac{4}{7 - 6t}, \\hspace{1cm} 0 < t \\le 1\n",
    "    \\end{cases}\n",
    "\\end{equation*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Аналитическое решение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Переменные разделяются, ищем решение в виде: $U = T(t)X(x)$\n",
    "\n",
    "$$T'X = T^2 \\frac{\\partial}{\\partial x} \\left(X \\frac{\\partial X}{\\partial x} \\right)$$\n",
    "\n",
    "Разделим на $T^2X$:\n",
    "\n",
    "$$ \\frac{T'}{T^2} = \\frac{\\frac{\\partial}{\\partial x} \\left(X \\frac{\\partial X}{\\partial x} \\right)}{X} = -k = const $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Рассмотрим первое уравнение:\n",
    "\n",
    "$$ T' + kT^2 = 0 \\hspace{0.5cm} \\Longrightarrow \\hspace{0.5cm} T = \\frac{1}{C_0 + kt}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Второе уравнение можно преобразовать:\n",
    "\n",
    "$$X\\frac{dX}{dx} = \\frac{1}{2} \\frac{dX^2}{dx} \\longrightarrow \\frac{d^2 (X^2)}{dx^2} + 2kX = 0$$\n",
    "\n",
    "Будем искать частное решение в виде полинома степени не выше 2:\n",
    "\n",
    "$$ X_{частн} = a_0 + a_1 x + a_2 x^2$$\n",
    "\n",
    "Подставим и выпишем коэффициенты при степенях $x$:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "    x^2 &: 4 a_2^2 + (2 a_2 + k) a_2 = 0    &\\longrightarrow& \\hspace{1cm} a_2 = -\\frac{k}{6}  \\\\\n",
    "    x   &: 4 a_1 a_2 + (2 a_2 + k) a_1 = 0  &\\longrightarrow& \\hspace{1cm} a_1 - любое \\\\\n",
    "    1   &: a_1^2 + (2 a_2 + k) a_0 = 0      &\\longrightarrow& \\hspace{1cm} a_0 = -\\frac{3 a_1^2}{2k}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Пусть $a_2 = 1$, тогда $k = -6$, $a_0 = a_1^2 / 4$\n",
    "\n",
    "$$X_{частн} = a_1^2/4 + a_1 x + x^2 = (a_1 + x)^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Получаем решение на $U$:\n",
    "\n",
    "$$ U = \\frac{(C_1 + x)^2}{C_0 - 6t} $$\n",
    "\n",
    "А с учетом граничных условий получаем следующее аналитическое решение:\n",
    "\n",
    "$$ U = \\frac{(1 + x)^2}{7 - 6t} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def u_analytical(x, t):\n",
    "    return (1 + x)**2 / (7 - 6*t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Численное решение"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Используется неявная разностная схема:\n",
    "\n",
    "$$\n",
    "\\frac{U_l^{k+1} - U_l^n}{\\tau}\n",
    "    = \\frac{(U_{l+1}^k + U_l^k)(U_{l+1}^{k+1} - U_l^{k+1})}{2 h^2}\n",
    "    - \\frac{(U_l^{k+1} + U_{l-1}^{k+1})(U_l^k - U_{l-1}^k)}{2 h^2},\n",
    "    \\hspace{1cm} l = \\overline{1, L-1}\n",
    "$$\n",
    "\n",
    "$$ U_0^n = \\frac{1}{7 - 6t^n}, \\hspace{1cm} U_L^n = \\frac{4}{7 - 6t^n}, \\hspace{1cm} U_l^0 = \\frac{(1 + x)^2}{7} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для решения этой системы из $L-1$ уравнений при переходе с $n$ временного слоя на $n+1$ будем использовать алгорит прогонки.\n",
    "\n",
    "Для начала нужно свести систему к трехдиагональной матрице. Представим систему в виде:\n",
    "\n",
    "$$ U_l^{k+1} - U_l^n = A_l(U_{l+1}^{k+1} - U_l^{k+1}) - B_l(U_l^{k+1} + U_{l-1}^{k+1}) $$\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "    A_l = \\frac{\\tau}{2h^2} (U_{l+1}^k + U_l^k) \\\\\n",
    "    B_l = \\frac{\\tau}{2h^2} (U_{l-1}^k + U_l^k) \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Снова переобозначая, получаем:\n",
    "\n",
    "$$ a_l U_{l+1}^{k+1} + b_l U_l^{k+1} + c_l U_{l-1}^{k+1} = d_l $$\n",
    "\n",
    "где:\n",
    "$$\n",
    "\\begin{cases}\n",
    "    a_l &= \\frac{\\tau}{2h^2} (U_{l+1}^k + U_l^k) \\\\\n",
    "    c_l &= \\frac{\\tau}{2h^2} (U_{l-1}^k + U_l^k) \\\\\n",
    "    b_l &= -(a_l + c_l + 1)                      \\\\\n",
    "    d_l &= -U_l^n\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "При прямом ходе прогонки сводим трехдиагональную матрицу к двухдиагональной. Прогоночное соотношение принимает следующий вид:\n",
    "\n",
    "$$ U_l = \\alpha_l U_{l+1} + \\beta_l \\hspace{1cm} l = \\overline{1, L-1}$$\n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "    \\alpha_1 &= -\\dfrac{a_1}{b_1}, \\hspace{1cm} &\\beta_1 = \\dfrac{d_1 - c_1 U_0}{b_1} \\\\\n",
    "    \\alpha_l &= -\\dfrac{a_l}{b_l + c_l \\alpha_{l-1}}, \\hspace{1cm} &\\beta_l = \\dfrac{d_l - c_l \\beta_{l-1}}{b_l + c_l \\alpha_{l-1}}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Значения $U_0^n, U_L^n$ известны из граничных условий, поэтому система легко решается.\n",
    "\n",
    "Нужно провести несколько этапов прогонки пока не достигентся нужная точность."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep_method(u, dt, h, u_left, u_right, epsilon=1e-4):\n",
    "    L = u.size\n",
    "    C = dt / (2 * h**2)\n",
    "    d = -u[1:-1]\n",
    "    \n",
    "    u_k = u\n",
    "    max_diff = epsilon + 1\n",
    "    \n",
    "    while max_diff > epsilon:\n",
    "        u0 = u_k[:-2]\n",
    "        u1 = u_k[1:-1]\n",
    "        u2 = u_k[2:]\n",
    "\n",
    "        a = C * (u2 + u1)\n",
    "        c = C * (u1 + u0)\n",
    "        b = -(a + c + 1)\n",
    "    \n",
    "        # forward run\n",
    "        alpha = [-a[0] / b[0]]\n",
    "        beta = [(d[0] - c[0] * u_left) / b[0]]\n",
    "\n",
    "        for l in range(1, L - 2):\n",
    "            alpha.append(-a[l] / (b[l] + c[l]*alpha[l-1]))\n",
    "            beta.append((d[l] - c[l]*beta[l-1]) / (b[l] + c[l]*alpha[l-1]))\n",
    "\n",
    "        # reverse run\n",
    "        u_next = np.empty(L)\n",
    "        u_next[0] = u_left\n",
    "        u_next[-1] = u_right\n",
    "    \n",
    "        for l in range(L - 2, 0, -1):\n",
    "            u_next[l] = alpha[l - 1] * u_next[l + 1] + beta[l - 1]\n",
    "        \n",
    "        max_diff = np.max(np.abs((u_next - u_k)[1:-1] / u_next[1:-1]))\n",
    "        u_k = u_next\n",
    "\n",
    "    return u_k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Общий ответ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def common_answer(L=11, N=11):\n",
    "    xs, h = np.linspace(0, 1, L, retstep=True)\n",
    "    ts, dt = np.linspace(0, 1, N, retstep=True)\n",
    "    \n",
    "    u_a = u_analytical(xs, np.ones(xs.size))\n",
    "\n",
    "    U = np.empty(shape=(N, L))\n",
    "    U[0] = (1 + xs)**2 / 7\n",
    "    U_0 = 1 / (7 - 6*ts)\n",
    "    U_L = 4 / (7 - 6*ts)\n",
    "\n",
    "    for n, t in enumerate(ts[1:], 1):\n",
    "        U[n] = sweep_method(U[n-1], dt, h, U_0[n], U_L[n])\n",
    "    u = U[-1]\n",
    "    \n",
    "    step_for_output = (L - 1) // 10\n",
    "\n",
    "    df = pd.DataFrame(\n",
    "        {\n",
    "            'Grid': xs[::step_for_output],\n",
    "            'Model analytical': u_a[::step_for_output],\n",
    "            'Model numerical': u[::step_for_output],\n",
    "        }\n",
    "    )\n",
    "    print('Значения в 11 равноудаленных точках:\\n')\n",
    "    print(df.to_string(index=False))\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(8, 6))\n",
    "    \n",
    "    ax.set_title(f'L={L}, N={N}')    \n",
    "    ax.plot(xs, u, '-r', label='numerical solution')\n",
    "    ax.plot(xs, u_a, '--k', label='analytical solution: $(1 + x)^2$')\n",
    "    ax.set_xlabel('$x$', fontsize=14)\n",
    "    ax.set_ylabel('$U(x, t=1)$', fontsize=14)\n",
    "    ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Значения в 11 равноудаленных точках:\n",
      "\n",
      " Grid  Model analytical  Model numerical\n",
      "  0.0              1.00         1.000000\n",
      "  0.1              1.21         1.327595\n",
      "  0.2              1.44         1.621458\n",
      "  0.3              1.69         1.903759\n",
      "  0.4              1.96         2.184122\n",
      "  0.5              2.25         2.467545\n",
      "  0.6              2.56         2.756890\n",
      "  0.7              2.89         3.053892\n",
      "  0.8              3.24         3.359647\n",
      "  0.9              3.61         3.674862\n",
      "  1.0              4.00         4.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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n53qntm5UuHBhevbsSd++fXnhhReoUKEC69evp169emTKlAmA+vXrs27duiTPKr3deV988cXbXjeARYsW3XKu0NBQsmfPnqD2S5cuzbVr17h06RJnzpy53t7w4cN5/vnn/3NsxYoVsdby8ccfExwcfP1f9gEBAaRNm5aLFy/SvXt3unfvnqAaRMTDrIVRo6BXLyhQgLAZM2g8eDA//PADw4YNo2fPnt6uMN5SXMB7Q3BwMCtWrGDTpk1kzJiRypUrExYWBkC6dOmuHxcQEMDVq1fjPP5G7dq1Y/Lkyfzzzz+88sorLq8tNo899hjbt29n0aJFDBw4kKpVq5ItW7Y7tpM6dWqio6Ov/xxXG/ER23WLS4YMGRLc5pYtWwDnGk2ePJnJkyff9tiff/6Z48ePkzNnTrJkyfKf965du+azk3BE5AZXrjj326dPhzp1uDxmDHVbtmTFihV8/vnndOnSxdsVJkiKC/i4etwZM2aM8/1cuXLFu8d+o/Pnz5MjRw4yZszI/v372bx5s0uOr1evHoMGDSIiIoLp06cDkCVLllh78c888wz16tXjjTfeIGfOnJw5c4a77rorwbUdO3aMu+66i+bNm5M9e3YmTJjAoEGDaN26Nf369cNay9y5c5k2bdp/PpcnTx5OnjzJ6dOnyZw5MwsWLKB69epx1lyhQoU7nje+cuTIQVRUFGFhYS4P2+PHj9OsWTN++OEHunfvzpIlS67/2k6fPk2uXLl8eiKOiAB//AH168Pu3fDOO/Dmm9grV7h27RqTJ0+mVatW3q4wwVJcwHtD9erVGTt2LAULFuTxxx+nTJkyLjk+bdq0VKlShezZs18fEs6ZMyfly5cnMDCQGjVq8OGHHwJQqFAhBgwYQKVKlQgICKBYsWJMnjw5wbX9/PPP9O7dm1SpUpEmTRrGjBlD8eLFad26NaVKlQKckYWbh+fTpEnDoEGDKFWqFPfffz9PPPHE9fdurvlftzvvjcPxsalZsyYTJkzgvvvu+8/r1apVY/369Tz77LMANGnShODgYEJDQ3nggQcYMmQIbdu2jfPcN7ty5Qr169fno48+omDBgrz11lv07dv3esCvXr2aWrVqJeicIuJhS5ZA06bO8PzChYSWLEm6y5fJkiULwcHBpEqVPOejG+f+vH8ICgqyISEh/3lt3759FCxY0EsVuVd0dDTFixfn+++/59FHH/V2OT5v+/btfPLJJ4keBUiM+vXrM2zYMB577LF4He/Pv19FfI618P77MHAgBAbC3Lkcy5CB5557joceeoiFCxdivLSXe0IYY7ZZa4Nufj15/rNE2Lt3LwUKFKBq1aoK93gqXrw4VapUub7QjbuFh4dTt27deIe7iHjQhQvQoAEMGACNG8OmTRwOCKBChQr89ddf9OnTJ1mEe1w0RJ9MPfnkk/zxxx/eLiPZSexkxMRImzYtLVu29Fh7IhJP+/dDvXrw22/wySfQowcHfv2VZ599lkuXLrFixQpKly7t7SqTTAEvIiIpx7x50LIlpE8PK1ZA5cpYa2nSpAnh4eGsWbOGp556yttVuoQCXkRE/F9UFAwaBO+9ByVLwuzZ8OCDABhj+PrrrwkICODxxx/3cqGuo3vwIiLi386cgRdecMK9XTtYuxYefJA1a9bQv39/rLU8+eSTfhXukEIC3p+eFBD/pd+nIm6waxcEBcHKlfDllzB+PKRPf329innz5nHhwgVvV+kWfh/w6dOn5/Tp0/rLU3yatZbTp09rxTsRV5o+HcqWdXaEW7sWOnQAYPbs2bz44osULFiQNWvWxGs1zuTI7+/BP/DAAxw9epRTp055uxSROKVPn54HHnjA22WIJH8REdCnD4wcCRUqwHffwT33ADBt2jRat25NmTJlWLhwYYL3qEhO/D7g06RJQ/78+b1dhoiIeMKJE9CoEaxZA927w4gRcMNS0ZkzZ6ZatWp8//33/9ma2h/5/RC9iIikEFu3QokSsGULTJvm7AoXE+779u0DnD08Fi1a5PfhDgp4ERFJ7qyFsWOd4fg0aWDjRmjePOYty1tvvUXhwoWv7xCZ3Feoiy+/H6IXERE/dvkydOwI33wDNWo4PfecOQEn3N944w1GjhxJu3btCAq6Zbl2v6YevIiIJE/790OpUs5s+f/9DxYsuB7uUVFRdOjQgZEjR9KjRw/GjRt3fdfNlEI9eBERSX5mznQWrcmQAZYtg5htoP81Z84cJkyYwMCBAxk6dGiKGZa/kQJeRESSj/Bw6NULRo+GcuWcoI/l8dKXXnqJFStWULVqVS8U6Rs0RC8iIsnDX39BxYpOuL/+OgQH/yfcL1++TOPGjdm7dy/GmBQd7qCAFxGR5GDpUiheHPbuhe+/h48//s/z7WfPnr3+fPvu3bu9WKjvUMCLiIjvioqCwYOdGfL33QchIfDSS/855MiRIzz99NOEhIQwc+ZMGjdu7J1afYzuwYuIiG8KDYVmzZxJdC1bwpgxkDHjfw45dOgQFStW5Pz58yxZsoQqVap4qVjfox68iIj4ns2boVgxZ8nZceNg8uRbwh3g3nvvpXz58qxdu1bhfhMFvIiI+A5r4dNP/7sqXfv2cNNjbsuWLePs2bOkT5+eGTNmULRoUe/U68MU8CIi4hsuXoTGjaFHD+ee+7ZtzsS6m4wfP54aNWrw1ltveaHI5EMBLyIi3vfLL1CyJMyaBcOGwbx5kCPHfw6x1jJ06FA6dOhAtWrVGDZsmHdqTSY0yU5ERLzr66+d9eSzZIGVK6Fy5VsOiYqKomvXrowdO5aWLVsyYcIE0tzwmJzcyis9eGNMemPMVmPMLmPML8aYIbEc09oYc8oYszPmq503ahURETcJC4POnaFFCwgKgh07Yg13gDNnzrB48WL69OnD5MmTFe7x4K0e/DXgGWvtJWNMGmC9MWaxtXbzTcfNtNZ29UJ9IiLiTocPO8+zb9sGvXvDe+9B6lsj6cKFC2TKlIncuXOzY8cOctw0bC+355UevHVcivkxTcyX9UYtIiLiYQsXOpPnDh6EuXPhgw9iDfe///6b8uXL89prrwEo3BPIa5PsjDEBxpidwElgubV2SyyHNTDG7DbGzDLGPOjZCkVExKWiomDAAHjhBXjoIaf3XrdurIfu27ePsmXL8ueff1L3NsdI3LwW8NbaKGttUeABoJQxJvCmQ34E8llrnwKWA1NiO48xpoMxJsQYE3Lq1Cm31iwiIol04gRUq+YMxbdt6zzf/sgjsR66adMmnn76acLDw1mzZk2K3zQmsYy13h8ZN8YMAq5Ya0fc5v0A4Iy1Nltc5wkKCrIhISHuKFFERBJr/Xpo2BDOnoUvvoA2bW576KVLl8ifPz/Zs2dn6dKlPPzwwx4sNHkyxmyz1gbd/Lq3ZtHnNsZkj/k+A/AcsP+mY+694ccXgX0eK1BERJLOWvjoI2dmfKZMzvKzcYQ7QObMmfn+++/ZsGGDwj2JvDWL/l5gSkzPPBXwnbV2gTFmKBBirZ0PdDfGvAhEAmeA1l6qVUREEur8eSfM586F+vVh0iTIFvsgrLWW9957j1y5ctGxY0cq3+ZROUkYnxiidxUN0YuI+IBdu5xH4A4dcmbIv/76LWvJ/ysqKooePXrw+eef07JlSyZPnoy5zbESO58aohcRET/11VdQpgxcvgzBwfDGG7cN97CwMBo3bsznn39Oz549+eqrrxTuLqSlakVEJOmuXoVu3WDiRHjmGZg+HfLkue3hkZGR1KhRg+DgYEaMGEHPnj09WGzKoIAXEZGk+f13Z0h+507o3x+GDoWAgDg/kjp1amrWrEm7du1o1qyZZ+pMYRTwIiKSePPmQevWkCoVLFgAtWrFefivv/5KaGgo5cqVo3fv3h4pMaXSPXgREUm4yEhnDfl69aBAAdi+/Y7hvmXLFsqVK0ebNm2IjIz0UKEplwJeREQS5vhx5z77iBHQqZOzkE2+fHF+ZPHixTzzzDNky5aNhQsXkjqWtefFtRTwIiISf8HBUKyYs478tGkwZgykTx/nR6ZMmULt2rV54okn2LhxIwUKFPBMrSmcAl5ERO4sOhqGDYOqVSF7dtiyBZo3v+PHrLUsXryYKlWqEBwcTJ44ZtaLa2mMRERE4nb6tDORbsECZ035CRMgS5Y4PxIdHc2ZM2fIlSsXU6ZMwRhD2rRpPVOvAOrBi4hIXNavh6JFYdky+PRTmDHjjuF+7do1mjRpQoUKFbh8+TLp0qVTuHuBAl5ERG4VHQ3vv+9sFJM2rbO9a7dut12V7l8XLlygZs2afPfdd7Rt25aMGTN6pl65hYboRUTkv06ehBYtnF57w4YwbtxtN4q50T///EONGjXYs2cPU6dOpUWLFh4oVm5HAS8iIv8vOBiaNoUzZ2DsWOjQ4Y699n916dKF3377jR9//JHq1au7t065IwW8iIhAVBS8+y4MGeIsXLN4MRQpkqBTfPHFFxw9epSgoFs2NhMv0D14EZGU7p9/oFo1ePttaNIEQkLiHe5LliyhSZMmREZGcs899yjcfYgCXkQkJVuxwgnzTZucneCmTbvjLPl/TZs2jdq1a7Nv3z7Onz/v5kIloRTwIiIpUWQkDBzo9Nxz5YKffoJXXonX/XZrLR9++CEtW7akYsWKrF27lpw5c3qgaEkIBbyISErz99/OinTvvussYLN1KxQqFO+PDx06lD59+tCwYUMWLVpE1qxZ3VerJJom2YmIpCSLF0PLlnD1Kkyd6jwOl0A1a9bk8uXLDBs2jFSp1E/0Vfo/IyKSEkREQN++ULMm3HuvM5EuAeF+8eJFpkyZAkDJkiX54IMPFO4+Tv93RET83V9/QaVK8MEH0LGjs1HME0/E++NHjx6lQoUKtG3blv3797uxUHElDdGLiPiz+fOd++yRkfDtt9C4cYI+vm3bNmrXrs2lS5dYsGABTyTgHwbiXerBi4j4o/BweOMNqFMH8ueH7dsTHO4//PADFStWJE2aNGzcuFGr0yUzCngREX9z6BA8/TR88omzQczGjc7qdAl0+fJlChcuzJYtWwgMDHRDoeJOCngREX8yZw4UKwa//gqzZztbvKZLF++PR0REsHnzZgCaNm3Khg0buOeee9xVrbiRAl5ExB+EhTm99QYN4LHHYMcOqF8/Qac4f/48tWrVolKlSvz5558ABAQEuKNa8QBNshMRSe4OHnS2dd2xw7nv/v77zh7uCXDo0CFeeOEFfv31V8aNG8dDDz3kpmLFUxTwIiLJ2YwZzpauqVM7M+Zr107wKTZt2kSdOnWIiIhg2bJlVKlSxQ2FiqdpiF5EJDm6etV5pr1JEyhcGHbuTFS4AyxYsICsWbOyefNmhbsfMdZab9fgMkFBQTYkJMTbZYiIuNf+/c6Q/M8/O6vT/e9/kCZNgk5hreXYsWPcf//9REdHc/78eXLkyOGmgsWdjDHbrLW37NOrHryISHIybRoEBcHx48668sOGJTjcr127RuvWrSlRogQnT54kVapUCnc/pIAXEUkOLl+GNm2cjWJKlHCG5BOx8Mzp06epVq0aU6dO5dVXXyV37tyur1V8gibZiYj4ul9+cYbk9+2Dt96CQYOcSXUJ9Ouvv1KrVi3++usvpk+fTpMmTdxQrPgKBbyIiK+yFr76Crp2haxZYdkyePbZRJ9u6NChnDt3jlWrVlG+fHkXFiq+SAEvIuKLLl6Ezp3hm2+galX4+mtI5IpyYWFhpE+fnjFjxhAaGkr+/PldXKz4It2DFxHxNbt2ORPpvv0Whg6FpUsTFe7R0dEMHDiQp59+msuXL5MlSxaFewqigBcR8RXWwpdfQunScOkSrFrl3HNPxHKxV69epWnTprz77rsULVqUtAlc2U6SPw3Ri4j4ggsXoH17+O47Z3b81KmQyBnuJ0+epE6dOmzevJkPPviAXr16YYxxccHi6xTwIiLe9tNPzop0hw87z7X37g2pEj/A2qZNG3bt2sXs2bOpn8ANZ8R/KOBFRLwlOhpGjIABA+Dee2HNGkjC7HZrLcYYRo8ezenTpylZsqQLi5XkRvfgRUS84fhxeP55Z6nZunWdiXVJCPdx48bRqlUrrLU8/PDDCnfxTsAbY9IbY7YaY3YZY34xxgyJ5Zh0xpiZxpiDxpgtxph8XihVRMT1FiyAp56CjRth/Hjnvnsil4qNioqiV69edOzYkdDQUMLCwlxcrCRX3urBXwOesdYWAYoC1Y0xZW46pi1w1lpbAPgEGO7ZEkVEXCwsDLp3d3Z9u/9+2LYN2rWDRE6Au3z5Mg0aNOCjjz6ia9euzJ8/nwwZMri4aEmuvBLw1nEp5sc0MV83b2tXB5gS8/0soKrRNFARSa727XMefxs9Gnr0gM2b4YknEn06ay1169blxx9/5NNPP2X06NGkTsTyteK/vHYP3hgTYIzZCZwElltrt9x0yP3AEQBrbSRwHsgZy3k6GGNCjDEhp06dcnPVIiIJZC2MG+dsEHP8OCxcCCNHQvr0STqtMYb+/fszf/58unXr5ppaxa94LeCttVHW2qLAA0ApY0xgIs8zzlobZK0N0q5IIuJTzpyBl16Cjh3h6aediXQ1aybplAsWLOCTTz4BoEqVKtSqVcsVlYof8vosemvtOWA1cPO+h38DDwIYY1ID2YDTHi1ORCSx1q6FIkXgxx/hww9hyRLnUbhEstYyatQo6tSpw7fffkt4eLgLixV/5K1Z9LmNMdljvs8APAfsv+mw+UCrmO9fAlZZa2++Ty8i4lsiI+Htt6FKFWcYfuNG6NUrSQvXREZG0q1bN1577TXq1KnD6tWrtfSs3JG3ZmTcC0wxxgTg/CPjO2vtAmPMUCDEWjsfmAhMM8YcBM4Ajb1Uq4hI/Pz5JzRrBhs2QKtWzoS6LFmSdEprLfXq1WPBggX07t2bYcOGkSoJ/1iQlMP4U6c4KCjIhoSEeLsMEUmJvvsOOnRwJtWNHessPesiY8aMIXXq1LRv395l5xT/YYzZZq0Nuvl1PVMhIpIUly87j71NnAhlysD06eCCLVm3bt3KmTNnqF69Op07d3ZBoZLSaJxHRCSxduxwHn+bNAn693cm1rkg3GfNmkWlSpXo27cvUVFRLihUUiIFvIhIQkVHwyefOD32ixdh5Up4911IkyZJp7XWMnz4cF5++WWKFy/OihUrCEjEXvAioCF6EZGEOXECWrd2HnurU8cZms95yxpcCRYVFUWHDh2YNGkSjRs35quvviJ9EhfDkZRNPXgRkfhautR5tj04GD7/HObOdUm4A6RKlYqAgAAGDRrE9OnTFe6SZOrBi4jcybVrzj32jz+GQoVgxQoITNTim7fYvXs3qVKlIjAwkC+//BJtuSGuoh68iEhcfv0VypVzwr1LF/jpJ5eF+3fffUfZsmXp0qULgMJdXEoBLyISG2vhq6+geHE4fBjmzXOG5V2wHWtUVBRvvvkmjRo1omjRosycOTPJ5xS5mYboRURudu4cdOoEM2dC5crw9dfO/u0ucOHCBRo1asSSJUvo0KEDo0eP1rKz4hbqwYuI3GjjRihaFGbNch59W7HCZeEOkD59esLDwxk7dixffvmlwl3cRj14ERGAqCh47z0YMgTy5oX1653n3F1kwYIFlClThly5crF8+XKtJy9up99hIiJHj0LVqjBoEDRs6KxQ56Jwj46OZtCgQdSuXZt3330XQOEuHpHgHrwxJh1wH5ABOGWtPeXyqkREPGXuXGjbFsLDYfJkaNkSXDSb/fz58zRv3pwFCxbQpk0b3n//fZecVyQ+4vXPSGNMFmNMZ2PMWuA8cBDYA/xjjPnLGDPeGFPSnYWKiLjUlSvQuTPUrw8PP+z02lu1clm4Hzx4kNKlS7NkyRI+++wzJk6cqMVrxKPu2IM3xrwBDAD+AOYD7wLHgKvAXUAgUAFYbozZDHSz1v7mtopFRJLq55+hcWPYuxd694Z33gEXT3bLmjUrWbJkYeXKlVSsWNGl5xaJj/gM0ZcBKllr99zm/a3AJGNMJ6AtUAlQwIuI77HWeZa9Vy/IkQOWLYPnnnPZ6aOjo5k6dSrNmjXj7rvvZuvWrVq8RrzmjgFvrW0YnxNZa68BXyS5IhERdwgNhVdegR9/hJo1nUVs7r7bZae/ePEiLVu2ZN68eaROnZrmzZsr3MWr9JiciPi/lSuhRQs4fRpGjoTu3V12rx3gt99+o27duhw4cICRI0fSrFkzl51bJLFc8qyGMeZBY8wkV5xLRMRlrl1zhuOffRayZoUtW6BHD5eG+4oVKyhZsiQnTpxg6dKl9OjRQz138QmuehjzLqCVi84lIpJ0e/ZAqVLw0UfObPnt250V6lwsV65cFCpUiJCQEKpWrery84skVryG6I0xLe9wSF4X1CIiknTR0TB6NPTt6/Taf/wRXnjBpU1cunSJ77//njZt2lC0aFHWr1+vXrv4nPjeg58MXAHsbd7Xskwi4n3HjkGbNs7s+BdegAkTIE8elzbxxx9/ULduXX755RdKlixJYGCgwl18UnyD+RjQ0lqbJbYvoLwbaxQRubM5c6BwYVi3DsaOhfnzXR7uy5cvJygoiKNHj7J48WICXbQvvIg7xDfgtwHF43jfAvonrIh43sWLzlKzDRpA/vzOinQdO7p0Ih3A6NGjqV69Ovfffz8//fQT1apVc+n5RVwtvgE/AtgQx/sHgSpJL0dEJAE2b4ZixZw15AcMcLZ6ffxxtzR17733Ur9+fTZt2sQjjzziljZEXMlYe7vb6slPUFCQDQkJ8XYZIuJukZHO8rLvvAMPPADTpkGFCi5v5vDhw4SEhPDSSy8BYK3V/XbxOcaYbdbaoJtf10I3IpK8HDwIzZs7z7S3aOHMmM+WzeXNrFq1ioYNG5IqVSqef/55smTJonCXZEWz30UkebAWJk50nmU/cABmzICpU10e7tZaRo4cSbVq1bj77rtZv349WbJkcWkbIp6ggBcR3xca6kyia9cOSpd2doNr1MjlzVhradOmDa+//jq1a9dm8+bNPPbYYy5vR8QTEhzwxpjyxph0N38vIuIWS5c6j78tXAgjRsDy5c59dzcwxpAvXz6GDBnC7NmzyZo1q1vaEfGEBE+yM8ZcAIpaa/+48Xu3VJdAmmQn4keuXoV+/eDTT+HJJ2H6dChSxC1NrVu3DoAKbpioJ+Jut5tkl5ghenOb70VEXGPXLihZ0gn3Hj0gJMQt4W6t5fPPP+eZZ55hwIAB+NNTRSK6By8iviM62hmGL1XK2dp1yRJne9cMGVzeVFhYGO3ataNr1648//zz/Pjjj5olL35Fj8mJiG84cgRatYLVq6FePRg3DnLlcktT586do3r16mzZsoWBAwcyZMgQUqVSf0f8iwJeRLxv5kzo1AkiIpxH4dq0cflSszfKmjUrjz76KL1796ZBgwZua0fEmxTwIuI9589Dt27OSnRlysDXX4Mbl4GdNGkSVatW5aGHHmLatGlua0fEF2hMSkS8Y906Z+Lc9OkweLDzs5vCPTw8nE6dOtG2bVtGjhzpljZEfI168CLiWeHhMGQIDBvm7P62bh2ULeu25o4cOUKjRo3YtGkTffv25d1333VbWyK+JDEB/x5wJpbvRUTiduAANGsG27Y5W7x+8gm4cRnY7du3U61aNa5du8bMmTNp2LCh29oS8TUJHqK31r5vrT138/ciIrdlLYwd62zteugQzJ4NEya4NdwBHn/8cZ599lm2bdumcJcUxyv34I0xDxpjVhtj9hpjfjHG9IjlmMrGmPPGmJ0xX4O8UauIJNHJk/Dii9C5s7Ol688/Q/36bmvu2LFjtGvXjsuXL5MpUyZmzJih9eQlRfLWJLtIoKe19kmgDPCqMebJWI5bZ60tGvM11LMlikiSLVjgrCO/fDmMGgWLF8N997mtueXLl1O0aFG+/fZbduzY4bZ2RJKDBAW8MWaPMSbJezNaa49ba7fHfH8R2Afcn9TzioiPuHIFunSB2rXhnnuce+7du4ObFpOJiori7bff5vnnn+fuu+8mJCSEp59+2i1tiSQXCf3T9iRwy+5xxphsxpjPE1OAMSYfUAzYEsvbZY0xu4wxi40xhRJzfhHxsG3boHhxGDMGevWCrVuhkHv/+Pbs2ZOhQ4fSqlUrtmzZQsGCBd3ankhyEK9Z9MaYxcBWwAIPAidvOiQj0BF4NSGNG2MyA7OB16y1F256ezvwkLX2kjGmJjAPeDSWc3QAOgDkzZs3Ic2LiCtFRcEHH8CgQZAnD6xcCc8849YmrbUYY+jRowfFihWjVatWbm1PJDmJ13axxpgPgFJARZyQvwjsAnYAu4EngCbW2gfj3bAxaYAFwFJr7cfxOP4wEGStDb3dMdouVsRLDh+Gli2dZ9obNnRmzOfI4bbmoqOjee+999i5cyfff/+9NomRFO1228XGqwdvre0Tc5JrQFngPqBozFetmPP0SUAxBpgI7LtduBtj7gFOWGutMaYUzu2E0/FtQ0Q8wFpnedmuXZ3vp06F5s3duo78qVOnaN68OcuWLaNZs2aEh4eTLt0tdw5FUryELnST2VobgTN8viAJ7ZYHWgA/G2N2xrzWH8gLYK0dC7wEdDbGRAJXgcZWmzWL+I7QUOjYEebMgaefdtaTz5fPrU2uW7eOxo0bc/r0acaNG0e7du3Uexe5jQQFfEy4J5m1dj0Q559Ka+1nwGeuaE9EXGzBAmjXDs6ede67v/EGBAS4tcmwsDCaNGlCpkyZWLRoEUWKFHFreyLJndaiF5H4u3jRCfMJE+Cpp2DZMue/bnT27FmyZs1K+vTpWbBgAQ8//DBZs2Z1a5si/kC7yYlI/Kxf7+z+NmkS9OvnPP7m5nDftGkTRYoU4Z133gGgaNGiCneReFLAi0jcrl2Dvn2hYkVn8tzatfD+++DGiW3WWj7++GMqVqxI6tSpqVWrltvaEvFXLhuiN8bkBY5aa6NddU4R8bLdu6FFC+e/7dvDRx+5fYOYs2fP0qZNG3744Qfq1avHpEmTyJ49u1vbFPFHruzBHwZ2GWMquPCcIuINUVEwfDgEBcGJE86kunHj3B7uAAcPHmT58uV88sknzJ49W+EukkiunGT3CpAfGAGUduF5RcST/vjDWbRmwwZo0MBZtCZXLrc2aa1l3bp1VKxYkZIlS/Lnn3+Sy81tivi7hG42k/t271lrJ1tr37bWKtxFkiNrYfx4Z+Lcnj3Oc+3ff+/2cD9//jwNGzakUqVKrFu3DkDhLuICCR2i32iMedgtlYiI9/zzj7Nne4cOULq0s2e7m1ekA9ixYwclSpRg7ty5fPDBB5QvX96t7YmkJAkN+EU4IV/8xheNMRWNMRtcV5aIeMycORAYCCtWOHu2L18OD8Z7W4lEmzRpEmXLliUsLIw1a9bQu3dvUrlpO1mRlChBf5qstT1w7rGvMsZUM8YUNcYsAVYDf7mjQBFxk/PnnXvtDRo4S8xu3+7WPdtvZoyhcuXK7NixQz13ETeI125yt3zImL7A/3CWm50HDLbW/uLa0hJOu8mJxNOqVdC6NRw7BgMGwMCBkCaN25vdvXs3Bw8epH79+oCzK5x67SJJc7vd5BI6ye5BY8yXwFDgJ+AasNAXwl1E4uHqVXjtNahaFTJkgI0bYcgQt4e7tZaJEydSunRp+vTpQ0SEs62Fwl3EfRL6p+s3oBjwgrW2PPAiMNIYM8DllYmIa23bBiVKOPfZu3aFHTugVCm3N3v58mVatWpFu3btKF++PBs2bCCNB0YLRFK6hD4H38xaO/vfH6y1q4wxlYBFxpj7rbVdXFueiCRZZCS89x7873+QJ4+zQcxzz3mk6cuXL1OqVCn27dvH4MGDGThwIAFu3nVORBwJ3S52diyv7TLGlAMWu6wqEXGNAweciXRbt0LTpvDZZ5Ajh8eaz5QpEw0bNuTpp5+matWqHmtXROIxRG+MyX+nY6y1fwLljcP9z9eISNyio50wL1YMDh6EmTPhm288Eu5Xr16lY8eObN26FYC3335b4S7iBfG5B7/JGDPRGFP2dgcYY3IAjYG9QB1XFSciiXD0KFSvDt26QeXKzqI1DRt6pOkDBw5QunRpxo0bx8aNGz3SpojELj5D9E8AA4CFxphoYBtwDAgDcgBPAgWBrcBr1tqlbqpVRO7k22+hSxcID4cxY6BjR7evRvf/TX9Lhw4dSJcuHYsXL6Z69eoeaVdEYnfHHry19py1tjdwP9AJ2Adkx9lYJhKYAhSz1pZXuIt4yZkz0Lixc5/9iSdg507o1Mlj4f7jjz/StGlTihQpws6dOxXuIj4g3pPsrLVXgVkxXyLiK5YsgVdegVOn4N13oU8fSO3KjSJvLywsjPTp01OzZk3GjBlD27Zt9QiciI+I13Pwxpg/jTGzjDH9jDHPxtxzFxFvunwZOneGGjXgrrucmfL9+3sk3KOjo/n444957LHHOHHiBAEBAXTq1EnhLuJD4rvQzRQgI/A6sAwINcb8YYyZZoyp5bbqRCR2mzZB0aLw5ZfQsyeEhDgz5j3g77//plq1avTs2ZPixYvruXYRHxWvgLfWDrLW1rTW5gHyAS8D3wKPA/ONMXONMZ4ZExRJycLDnbXjn34aIiJg9WoYMQLSp/dI87NmzaJw4cJs2rSJcePGMXfuXO3dLuKjErwQtLX2L2vtHGvtAGttKaAsUBLo6PLqROT//fILlCnjrErXqhXs3g2VKnmseWst06dPp0CBAuzYsYP27dtjPDSJT0QSLsm9bmvtVmPMW0BX4POklyQi/xEdDZ984vTcs2aFefOgjueWm9i0aRO5c+emQIECTJ48mQwZMuheu0gy4KqtnEKAR1x0LhH51+HD8Mwz0KsXPP887NnjsXCPjIxk8ODBVKhQgf79+wOQNWtWhbtIMhGvHrwxpifO9rDbrbWXYjkkD87WsSLiCtbCxInw+uvOs+yTJjn7t3toSPzgwYM0b96cLVu20KJFC0aPHu2RdkXEdeI7RP8mcBcQbYz5DafHHgLsATIA7wJr3FKhSEpz/Di0bw8LF0KVKvDVV/DQQx5rfsOGDTz//POkSZOGGTNm0KhRI4+1LSKuE6+At9bmMsY8BJS44WsgkDPmkH1Ab7dUKJKSzJjhLDV79er/79ueylV30uKnWLFiNGrUiMGDB/Pgg9o7SiS5ivffHNbaP2+YPV/dWpsbeAB42FpbKGZHORFJjNOnoVEjaNIEHnvMWWq2e3ePhfvy5cupUqUKly9fJmPGjEycOFHhLpLMJelvD2vtMWvtYRfVIpIyLVwIgYEwd66z1Oz69fD44x5pOiwsjNdff51q1apx4sQJTpw44ZF2RcT9PDv2JyL/78IFaNsWXngBcueGn37y2FKzAD///DOlSpVi5MiRdO3alZCQEB5++GGPtC0i7qfV50S8YfVqaNMGjhyBfv1g8GBIl86jJXTv3p2TJ0+yaNEiatSo4dG2RcT9FPAinnT1Krz5pjOBrkABWLcOypXzWPPHjh0jbdq05MqViylTppA+fXruvvtuj7UvIp6jIXoRT9m61dkQ5t/Z8Tt3ejTc58yZQ+HChenatSsAefPmVbiL+DEFvIi7hYfDW285YX7lCixfDqNHQ6ZMHmn+0qVLtG3blgYNGvDwww8zZMgQj7QrIt6lIXoRd/r5Z2jZ0umtt2rl9N6zZfNY83v27KFu3br88ccf9O/fn8GDB2upWZEUQgEv4g5RUc42roMGQfbsHt8g5l958uQhV65cfPXVV1SoUMHj7YuI92iIXsTVDh6EihWd2fG1a3t0gxiAP/74g27duhEZGUnu3LnZtGmTwl0kBVLAi7hKdDR8/jkUKQJ798LXX8P33zvPuHuAtZbJkydTpEgRpk2bxr59+wC0Z7tICqWAF3GFI0ec7Vy7doUKFZxee7NmHtv97fTp0zRs2JA2bdpQokQJdu/eTeHChT3Stoj4Jq8EvDHmQWPMamPMXmPML8aYHrEcY4wxnxpjDhpjdhtjinujVpE4WQtTp0LhwrBpE4wdC4sXw/33e7SMl156iR9++IFhw4axcuVK8ubN69H2RcT3eGuSXSTQ01q73RiTBdhmjFlurd17wzE1gEdjvkoDY2L+K+IbTp6Ejh2dCXRPPw2TJ8Mjj3is+WvXrhEdHU2GDBn46KOPACheXP8OFhGHV3rw1trj1trtMd9fxNlu9uYuTx1gqnVsBrIbY+71cKkisZszBwoVgkWL4MMPITjYo+G+Z88eSpUqRa9evQAn2BXuInIjr9+DN8bkA4oBW256637gyA0/H+XWfwRgjOlgjAkxxoScOnXKbXWKAHD2LLRoAQ0aQN68sH079OoFAQEeaT46OppRo0YRFBTEP//8Q82aNT3SrogkP14NeGNMZmA28Jq19kJizmGtHWetDbLWBuX20GxlSaGWLXPutX/7Lbz9Nmze7PTiPeT48ePUqFGD1157jeeee46ff/6ZWrVqeax9EUlevBbwxpg0OOH+jbV2TiyH/A08eMPPD8S8JuJZly5Bly7OLPmsWZ1gHzwYPLwi3KVLl9ixYwdjxoxh/vz5WkdeROLkrVn0BpgI7LPWfnybw+YDLWNm05cBzltrj3usSBGA9euhaFFndvwbb8C2bRAU5LHmz58/z5gxY7DW8uijj3L48GE6deqkZ9tF5I68NYu+PNAC+NkYszPmtf5AXgBr7VhgEVATOAhcAdp4vkxJscLCnGVmR4yAfPmcSXQVK3q0hMWLF9OhQweOHTtGqVKlKFGiBBkzZvRoDSKSfHkl4K2164E4uyDWWgu86pmKRG6wfbuzQcwvv0CHDk7IZ8nisebPnDnD66+/ztSpUylUqBCzZ8+mRIkSHmtfRPyDNpsR+VdEBLz/Pvzvf87ysosWQY0aHi3BWkvVqlX5+eefGThwIAMHDiRdunQerUFE/IMCXgRg3z6n1x4SAk2bOvu133WXx5oPDQ0le/bspE6dmg8//JCcOXNSrFgxj7UvIv7H68/Bi3hVdDR8/DEUKwaHDjmbw3zzjcfC3VrLzJkzKViwICNGjADg2WefVbiLSJIp4CXlOnwYnnkGevaEatWcDWJeesljzf/zzz80aNCAxo0bkz9/fl544QWPtS0i/k8BLymPtTBpEjz1lDOhbtIk+OEHuOcej5Uwf/58nnzySRYtWsTw4cPZuHEjgYGBHmtfRPyf7sFLynLiBLRvDz/+CJUrOxvEPPSQx8vIkycPgYGBjB8/nscff9zj7YuI/1MPXlKOOXMgMNBZcvaTT2DlSo+Fu7WW8ePH069fPwBKly7NmjVrFO4i4jYKePF/5845M+QbNHACfft2eO01SOWZ3/6HDh3iueeeo0OHDoSEhBAREQGg1ehExK0U8OLfVqxwNoiZPt3ZIGbTJnjySY80HR0dzWeffUbhwoXZunUrY8eOZdmyZaTx8Br2IpIy6R68+KcrV6BfP+d59scfd4K9ZEmPlnD06FH69u1LhQoVGDduHHnz5vVo+yKSsqkHL/5n61bnufbRo6FHD2dI3kPhHhUVxezZs7HWkjdvXkJCQli8eLHCXUQ8TgEv/iMiwtkgplw5uHrVmUQ3ciR4aIOWvXv3Ur58eV566SVWr14NQMGCBXWvXUS8QgEv/mHvXihTxllHvlkz+PlnZxEbD4iIiOC9996jWLFiHDx4kOnTp1OlShWPtC0icju6By/JW3S000vv39/Z8W3OHKhXz6Ml1KtXj4ULF/Lyyy/z2Wefcffdd3u0fRGR2CjgJfk6fBhat4Y1a+DFF2HcOMiTxyNNh4eHkypVKlKnTk3nzp1p06YNDRo08EjbIiLxoSF6SX5uXmr2q69g3jyPhXtISAglSpS4vjlMrVq1FO4i4nMU8JK8nDgBdepA27ZQooRzr711a/DARLawsDD69etH6dKlOXPmDIULF3Z7myIiiaUhekk+5syBjh3h4kVnqdnu3T22Gt1PP/1EixYtOHDgAG3btmXEiBFkz57dI22LiCSGAl5837lzTphPm+b02qdO9dhqdP+Kjo4mIiKCZcuW8dxzz3m0bRGRxNAQvfg2Ly41GxwczDvvvAM4m8McOHBA4S4iyYYCXnzTlStOr/255yBTJifYBw8GD6zjfvHiRV599VWqVKnClClTuHTpEgCpU2vAS0SSDwW8+B4vLjW7bNkyAgMDGTNmDK+//jq7du0ic+bMHmlbRMSV1CUR3xER4axE9957cN99zlKzHlqNDuD06dPUr1+fBx98kA0bNlC2bFmPtS0i4moKePENe/dCixZOb71lS/j0U8iWzSNNb9q0iTJlypAzZ06WLVtG8eLFSZ8+vUfaFhFxFw3Ri3dFR8PHH0Px4vDXX86jcFOmeCTcjx07RuPGjSlXrhzz5s0DoFy5cgp3EfEL6sGL93hpqdnIyEg+//xz3nrrLcLDwxkyZAi1atVye7siIp6kgBfPs9ZZXva115yfv/oKWrXyyGp0AHXr1mXhwoVUr16dzz77jEceecQj7YqIeJICXjzrxAlo3x5+/BEqV4bJk+Ghh9zebGhoKFmyZCFdunR07tyZV155hXr16mmvdhHxW7oHL54zZw4EBsKyZc5SsytXuj3co6OjGT9+PI8//jgfffQR4GwOU79+fYW7iPg1Bby437lzzsz4Bg2cQN++3Rmed/M68jt27KBcuXJ06NCBwMBA6tSp49b2RER8iQJe3GvlSmdbVw8vNTtq1CiCgoI4dOgQU6dOJTg4mEKFCrm9XRERX6GAF/e4dg169oRnn4WMGT2y1Ky1lrCwMADKli1Lp06d2L9/Py1atNBwvIikOJpkJ663bx80bQo7d0KXLvDhh07Iu9H+/ft59dVXKVCgAF9++SWlSpWiVKlSbm1TRMSXqQcvrmMtfPmls6Xr0aMwfz58/rlbw/3KlSsMGDCAp556iu3bt1OsWDG3tSUikpyoBy+uERoK7drBDz84O8BNmQL33uvWJjdv3kzjxo35888/adWqFR988AF33323W9sUEUkuFPCSdCtXOuvInz4NH33k9hny1lqMMdx3333cc889TJ06lYoVK7qtPRGR5EhD9JJ44eHQp4/TY8+WDbZsgTfecFu4X7t2jffee4969ephrSVv3rxs2rRJ4S4iEgsFvCTOgQNQtqwzga5DB9i2DYoWdVtzK1eupEiRIgwYMIDUqVNz9epVAM2OFxG5DQW8JIy1MGGCs/vbn3/C3LkwdqzbJtKFhobStGlTnn32WSIjI1m8eDGzZs0io5tn5YuIJHcKeIm/M2fgpZecteTLloXdu6FuXbc2mTZtWrZs2cLgwYPZs2cP1atXd2t7IiL+wisBb4yZZIw5aYzZc5v3KxtjzhtjdsZ8DfJ0jXKT1audFel+/BE++MBZT/6++9zS1MaNG2nUqBHh4eFkzZqVffv28fbbb2ufdhGRBPBWD34ycKeu2DprbdGYr6EeqEliEx4O/fpB1aqQKRNs3gy9e7tlIl1oaCjt2rWjfPnybNiwgd9//x1wevEiIpIwXgl4a+1a4Iw32pYE+O03KF8ehg93nnHfvt259+5i0dHRTJgwgccff5wpU6bQu3dv9u/fT8GCBV3elohISuHLz8GXNcbsAo4Bvay1v3i7oBTDWvjqK+jeHdKmhdmzoX59tzUXHR3NF198QaFChfjiiy8IDAx0W1siIimFr06y2w48ZK0tAowG5t3uQGNMB2NMiDEm5NSpU56qz3+dPQsNG0LbtlCqlDORzg3hfuHCBd58803OnDlD6tSpWbp0KWvWrFG4i4i4iE8GvLX2grX2Usz3i4A0xphctzl2nLU2yFoblDt3bo/W6XfWrHEm0s2bB8OGwfLl8MADLm3CWsuMGTN44oknGD58OEuXLgUgd+7ceqZdRMSFfDLgjTH3mJi/7Y0xpXDqPO3dqvxYRAQMGABVqkCGDLBxI/TtCwEBLm3mwIEDPPfcczRp0oT77ruPLVu20KRJE5e2ISIiDq/cgzfGfAtUBnIZY44CbwNpAKy1Y4GXgM7GmEjgKtDYWmu9UavfO3gQmjWDrVvhlVdg1CjInNktTQ0YMICQkBA+//xzOnbsSICL/wEhIiL/z/hTbgYFBdmQkBBvl5E8WAtTp0LXrpA6NYwf7yxi49ImLAsWLKBgwYIUKFCAY8eOERAQQJ48eVzajohISmaM2WatDbr5dZ8cohc3O3cOmjSB1q2dvdt373Z5uO/evZtq1arx4osv8tFHHwFw3333KdxFRDxEAZ/SrFsHRYo4j769+66z1euDD7rs9MePH6ddu3YULVqU7du3M2rUKD799FOXnV9EROJHAZ9SRETAW29B5cqQJg1s2AD9+7t8It2oUaOYOnUqr7/+OgcPHqR79+6kSZPGpW2IiMid6R58SvDHH85Eus2bnWH5Tz+FLFlccuro6Gi+/vpr8uXLR8WKFTl37hynT5/mkUceccn5RUQkbroHnxJZC9OmOfu079sHM2Y4K9S5KNyDg4MpWbIkrVq1YtKkSQBkz55d4S4i4gMU8P7q/Hmn196ypRPwu3ZBo0YuOfWvv/5K3bp1qVKlCqdOneLrr7++HvAiIuIbfHktekmsDRugeXM4cgT+9z94802X3mtfvnw5q1at4r333uO1114jQ4YMLju3iIi4hu7B+5PISHjnHSfUH3oIpk+HMmWSfNpr167x2WefkSdPHpo3b05ERARnzpzRI28iIj5A9+D93aFDUKkSDBniDM3v3JnkcLfWMmvWLJ588kl69erFihUrAEiTJo3CXUTExyng/cH06c599j17nO+nToWsWZN0yh07dlChQgVefvllMmbMyNKlS5k8ebJLyhUREffTPfjk7MIFePVV+PprKF/e+W++fC459bFjxzh48CDjxo3jlVde0brxIiLJjAI+udq7F+rWhd9/h8GDnd3gUif+f+eFCxd4//33yZAhA4MGDaJmzZr8/vvvZMqUyWUli4iI52iIPjmaMwdKl3Z68MHB8PbbiQ73yMhIxo4dS4ECBRg2bBhHjx4FwBijcBcRScYU8MlJVBQMHAgNGkChQrBtG1SokOjTbd68mSJFitC5c2cKFizITz/9xLhx41xYsIiIeIuG6JOLs2ed2fGLF0O7dvDZZ5AuXaJOFR0dTapUqciUKRNRUVHMnTuXOnXqYIxxcdEiIuItCvjkYM8e5377X3/B2LHQoQMkIoz/+ecf3nrrLcLCwpg2bRqFCxdm7969pEqlgRwREX+jv9l93fffO8+zX77s3G/v2DHB4X7lyhXeeecdChQowJQpU8idOzfR0dEACncRET+lHryv+vd++7BhULYszJoF992X4NNs3ryZl19+maNHj1K/fn2GDx9OgQIF3FCwiIj4EgW8LzpzBpo0gWXLnB77qFEJvt9++fJlMmXKRP78+Xn00UeZPn06FZIwIU9ERJIXBbyv2b0b6tWDo0dh3Dho3z5BH//111/p06cPJ06cYOPGjeTJk4dVq1a5qVgREfFVugHrS2bOdIbjw8JgzZoEhfvp06fp0aMHhQoVYuXKldSuXZvIyEg3FisiIr5MPXhfEBkJ/fvDhx86S87OmgX33BPvj//0009Uq1aNCxcu0K5dO4YOHarNYEREUjj14L3t9GmoUcMJ986dYdWqeIV7dHQ0hw8fBqBw4cLUqVOHXbt28eWXXyrcRUREAe9VO3dCUBCsXQsTJsAXX0DatHF+xFrLvHnzKFasGJUrVyY8PJz06dMzefJkAgMDPVO3iIj4PAW8t0yfDuXKQUQErFsHbdvGebi1lkWLFlGyZEnq1avH1atXeffdd7XLm4iIxEoB72mRkdCzp7PsbFCQs558qVJ3/NiqVauoVasWZ86c4auvvmLv3r00a9ZMAS8iIrHSJDtPCg2FRo2c++zdusFHH0GaNLc9fO3atRw+fJiWLVvyzDPPMGPGDOrVq0faOwzji4iIqAfvKdu3Oz32DRtg8mT49NPbhvvmzZt57rnnqFSpEu+99x5RUVEYY2jUqJHCXURE4kUB7wlff+08/hYdDevXQ6tWsR62b98+atWqRdmyZdm1axcfffQRO3bs0DC8iIgkmIbo3SkiAvr0gZEjoVIl+O47uPvuWw6LiooiICCAy5cvs2XLFoYNG8arr75K5syZPV+ziIj4BQW8u5w86dxvDw6GHj2c59xvGpLfu3cvgwcPJkuWLEycOJGgoCCOHDlChgwZvFOziIj4DQ3Ru0NIiHO/ffNmmDrV6cHfEO6//vorzZs3JzAwkMWLF/Pggw9irQVQuIuIiEuoB+9qU6dChw6QJ48zoa548f+8PW3aNNq0aUPatGnp3bs3vXv3JleuXF4qVkRE/JV68K4SEQHduzsT6MqXd3rxMeF+5MgRDhw4AECVKlXo3r07hw4dYvjw4Qp3ERFxCwW8K5w4Ac8+C6NHwxtvwNKlkDs3x48fp1u3bhQoUIAePXoA8MADD/Dxxx9rvXgREXErDdEn1U8/Qf36zqYx33wDTZty8uRJhg8fzhdffEFERARt2rRh4MCB3q5URERSEPXgk+Krr6BCBUidGjZuhKZNAZg0aRIjR46kYcOGHDhwgPHjx/PQQw95uVgREUlJFPCJER4Or74Kr7wCFSpwbuVK3p47l7lz5wLQtWtXfvnlF6ZMmcIjjzzi5WJFRCQlUsAn1D//wDPPwBdfcLFHD96tWJH8JUowdOhQNmzYAEDmzJl54oknvFyoiIikZLoHnxBbtjj328+eZXKnTvT+5htCQ0N54YUXGDp0KMWKFfN2hSIiIoB68PE3cSJhFSoQliYNbNpEQLlylChRgs2bN/Pjjz8q3EVExKd4JeCNMZOMMSeNMXtu874xxnxqjDlojNltjCke23EeER5OeIcOjGnXjgKpUjG6TRsoUoTmzZuzZMkSSpcu7bXSREREbsdbPfjJQPU43q8BPBrz1QEY44GabhHx119MfPJJHhs/ni5AvhIlKPPMMwAYY7xRkoiISLx4JeCttWuBM3EcUgeYah2bgezGmHs9U12MkBDaPP447X7/nTwFCrB06VLWrV9PhQoVPFqGiIhIYvjqJLv7gSM3/Hw05rXjNx9ojOmA08snb968rqsgZ056PPIIjTt3plaXLuqxi4hIsuKrAR9v1tpxwDiAoKAg67IT589PyZ9/BgW7iIgkQ746i/5v4MEbfn4g5jXPUriLiEgy5asBPx9oGTObvgxw3lp7y/C8iIiIxM4rQ/TGmG+BykAuY8xR4G0gDYC1diywCKgJHASuAG28UaeIiEhy5ZWAt9Y2ucP7FnjVQ+WIiIj4HV8dohcREZEkUMCLiIj4IQW8iIiIH1LAi4iI+CEFvIiIiB9SwIuIiPghBbyIiIgfUsCLiIj4IQW8iIiIHzLOonH+wRhzCvjThafMBYS68Hwpla5j0ukaJp2uYdLpGiadO67hQ9ba3De/6FcB72rGmBBrbZC360judB2TTtcw6XQNk07XMOk8eQ01RC8iIuKHFPAiIiJ+SAEft3HeLsBP6Domna5h0ukaJp2uYdJ57BrqHryIiIgfUg9eRETEDyngAWNMdWPMAWPMQWNMv1jeT2eMmRnz/hZjTD4vlOnT4nEN3zDG7DXG7DbGrDTGPOSNOn3dna7jDcc1MMZYY4xmNN8kPtfQGNMw5vfjL8aY6Z6u0dfF489zXmPMamPMjpg/0zW9UaevMsZMMsacNMbsuc37xhjzacz13W2MKe6WQqy1KfoLCAB+Bx4G0gK7gCdvOqYLMDbm+8bATG/X7Utf8byGVYCMMd931jVM3HWMOS4LsBbYDAR5u25f+orn78VHgR1Ajpif7/Z23b70Fc9rOA7oHPP9k8Bhb9ftS19ARaA4sOc279cEFgMGKANscUcd6sFDKeCgtfYPa204MAOoc9MxdYApMd/PAqoaY4wHa/R1d7yG1trV1torMT9uBh7wcI3JQXx+LwL8DxgOhHmyuGQiPtewPfC5tfYsgLX2pIdr9HXxuYYWyBrzfTbgmAfr83nW2rXAmTgOqQNMtY7NQHZjzL2urkMBD/cDR274+WjMa7EeY62NBM4DOT1SXfIQn2t4o7Y4/3qV/7rjdYwZynvQWrvQk4UlI/H5vfgY8JgxZoMxZrMxprrHqkse4nMNBwPNjTFHgUVAN8+U5jcS+ndmoqR29QlF4mKMaQ4EAZW8XUtyY4xJBXwMtPZyKcldapxh+so4I0lrjTGFrbXnvFlUMtMEmGyt/cgYUxaYZowJtNZGe7sw+X/qwcPfwIM3/PxAzGuxHmOMSY0zJHXaI9UlD/G5hhhjngUGAC9aa695qLbk5E7XMQsQCAQbYw7j3Lubr4l2/xGf34tHgfnW2ghr7SHgV5zAF0d8rmFb4DsAa+0mID3OGusSP/H6OzOpFPDwE/CoMSa/MSYtziS6+TcdMx9oFfP9S8AqGzNTQoB4XENjTDHgS5xw1z3P2MV5Ha215621uay1+ay1+XDmMrxorQ3xTrk+KT5/nufh9N4xxuTCGbL/w4M1+rr4XMO/gKoAxpiCOAF/yqNVJm/zgZYxs+nLAOettcdd3UiKH6K31kYaY7oCS3Fmj06y1v5ijBkKhFhr5wMTcYagDuJMnGjsvYp9Tzyv4YdAZuD7mPmJf1lrX/Ra0T4ontdR4hDPa7gUqGaM2QtEAb2ttRqRixHPa9gTGG+MeR1nwl1rdXr+nzHmW5x/ROaKmafwNpAGwFo7FmfeQk3gIHAFaOOWOvT/RERExP9oiF5ERMQPKeBFRET8kAJeRETEDyngRURE/JACXkRExA8p4EVERPyQAl5ERMQPKeBFRET8kAJeRBLFGPOSMeaaMeahG14bZYz53RiTx5u1iYhWshORRDLOmsM/ATuste2NMb2APkB5a+1v3q1ORFL8WvQikjjWWmuM6Q8sNMb8DvQHqircRXyDevAikiTGmI1AKaC2tXaxt+sREYfuwYtIohljngGKAAY44eVyROQG6sGLSKIYY4oAa4HXgVpAZmvt896tSkT+pYAXkQSLmTm/CRhrrR1qjAkEdgPPWGuDvVqciAAKeBFJIGPMXcAGYK21tuMNr88E8lpry3qtOBG5TgEvIiLihzTJTkRExA8p4EVERPyQAl5ERMQPKeBFRET8kAJeRETEDyngRURE/JACXkRExA8p4EVERPyQAl5ERMQP/R/aKx8VovZIXQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "common_answer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Значения в 11 равноудаленных точках:\n",
      "\n",
      " Grid  Model analytical  Model numerical\n",
      "  0.0              1.00         1.000000\n",
      "  0.1              1.21         1.214569\n",
      "  0.2              1.44         1.447133\n",
      "  0.3              1.69         1.698461\n",
      "  0.4              1.96         1.968931\n",
      "  0.5              2.25         2.258737\n",
      "  0.6              2.56         2.567978\n",
      "  0.7              2.89         2.896706\n",
      "  0.8              3.24         3.244948\n",
      "  0.9              3.61         3.612711\n",
      "  1.0              4.00         4.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "common_answer(L=51, N=333)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}