{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "06a1096d-9bf8-4801-b4af-589241f72489",
   "metadata": {},
   "source": [
    "PARTIE 1: MODELE DE COEUR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "ac5d86da-8153-459c-a669-8c994a752be8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "aa74a1d9-9422-45a3-bbde-606954523a12",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return (1/3)*(x**3)-x\n",
    "\n",
    "def dx_dt(t,x, y, epsilon):\n",
    "    return epsilon * (y - f(x)+Tfor*np.pi/5*np.sin(np.pi/5*t))\n",
    "\n",
    "def dy_dt(t,x, y):\n",
    "    return -x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "dd949ff4-256c-4b17-95e3-95b2c4ebc238",
   "metadata": {},
   "outputs": [],
   "source": [
    "def runge_kutta_4(x0, y0, t0, tf, dt, epsilon):\n",
    "    t = np.arange(t0, tf, dt)\n",
    "    n = len(t)\n",
    "    x = np.zeros(n)\n",
    "    y = np.zeros(n)\n",
    "    x[0] = x0\n",
    "    y[0] = y0\n",
    "    for i in range(1, n):\n",
    "        k1x = dx_dt(t[i-1],x[i-1], y[i-1], epsilon)\n",
    "        k1y = dy_dt(t[i-1],x[i-1], y[i-1])\n",
    "\n",
    "        k2x = dx_dt(t[i-1]+dt/2,x[i-1] + dt/2*k1x, y[i-1] + dt/2*k1y, epsilon)\n",
    "        k2y = dy_dt(t[i-1]+dt/2,x[i-1] + dt/2*k1x, y[i-1] + dt/2*k1y)\n",
    "\n",
    "        k3x = dx_dt(t[i-1]+dt/2,x[i-1] + dt/2*k2x, y[i-1] + dt/2*k2y, epsilon)\n",
    "        k3y = dy_dt(t[i-1]+dt/2,x[i-1] + dt/2*k2x, y[i-1] + dt/2*k2y)\n",
    "\n",
    "        k4x = dx_dt(t[i],x[i-1] + dt*k3x, y[i-1] + dt*k3y, epsilon)\n",
    "        k4y = dy_dt(t[i],x[i-1] + dt*k3x, y[i-1] + dt*k3y)\n",
    "\n",
    "        x[i] = x[i-1] + dt/6 * (k1x + 2*k2x + 2*k3x + k4x)\n",
    "        y[i] = y[i-1] + dt/6 * (k1y + 2*k2y + 2*k3y + k4y)\n",
    "\n",
    "    return t, x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "41af75aa-af10-4f28-ab90-64deaac17f8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Paramètres de simulation\n",
    "t0 = 0.0\n",
    "tf = 20.0\n",
    "dt = 0.004\n",
    "epsilon = 6\n",
    "Tfor=0; # pas de forcage (1 sinon)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "38e7ab51-9c6e-443f-b685-b5129e17e993",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exécution de la simulation\n",
    "t, x, y = runge_kutta_4(4, 2, t0, tf, dt, epsilon)\n",
    "t, x1, y1 = runge_kutta_4(-1, 3, t0, tf, dt, epsilon)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "b713b56c-d9d1-4954-ad74-0a176c3b4535",
   "metadata": {},
   "outputs": [
    {
     "data": {
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0SOPHj1dsbGzAt+8kjJX/GCv/MVb+Cek4lZQoJiVFLo9Hnq1bzR2XaKRgjVV5uXTkiHTokJSX51Jenv1oL0uHDrl0+LD9aD9X316S+sXEWEpJkVq3llq1kpKTrVOPUlKSpaQkKSmpcrnyucrnk5Ptr61pKIL5vsrPz1dqamq9pSbiDj/NmDFD7733npYsWVJnoZGk+Ph4xcfHV1sfGxsb1H/Iwd6+kzBW/mOs/MdY+Sck47Rhg+TxSCkpiu3VK2LPqfF3rNxuad8+32n//urrDh60i01DxcVJKSl1T23a1Ly+ZUvXacMfnL+LYLyv/N1exJQay7I0Y8YMvf3221q8eLG6R1jbB4BmqeL6NA44Sbi01C4ke/ZIOTn2dPr84cMN22abNlL79vaUmlo5X9tyYmLED2NQRUypmTZtmubNm6d3331XSUlJ2r9/vySpdevWatGiheF0AIAaRdiVhAsKpB07pJ077cdvvonSihWZuueeGOXkSGVl9W8jLk7q2NG+xVXF1Lmz73LHjnZJYYdiYEVMqZkzZ44kady4cT7r586dq5tvvjn0gQAA9Vu1yn4MoysJW5a0d6+0ZYv09de+j/v2nf7qaEkdvEsxMVKXLvblds48054q5tPTpTPOkNq2ZW+KKRFTaiLwfGYAaN7cbvvu3JI0bJiRCOXl9h6XNWvsae1a+7Guw0Tt2kk9ethTt25lKixcpyuvHKjevWPUsaMUHR26/GiYiCk1AIAIs369fZJwu3Yh+dSTZdkF5ssvfUtMQUH110ZHSz17Sn37Sn362FPfvlLv3vZ5LhU8nnLNn79Ho0adw6GiCECpAQAEx4oV9uOwYUE7HrNrl/TZZ9Lixfbjd99Vf01CgjRokJSRYZ/ac+650oABUg0fjkWEo9QAAIJj5Ur7MYCHnoqLpQULpPfft0vMt9/6Ph8bKw0fLg0dWllg+vSxz4WB8/HXDAAIjopSM3x4kzaTny998IH01lvShx9KJ05UPhcTY2/+ggvsKTPT/tgzmidKDQAg8AoK7I8USY3aU2NZ9p6Yv/9devdd+0aKFbp1k666SpowQRo50r7CLSBRagAAwbB6td1M0tOltDS/v+zYMWnuXLvMbNtWub5PH+n737enwYP5yDRqRqkBAARexUnCfh56On5ceuop6U9/sucl+55DU6dKP/2pfaIvUB9KDQAg8Pw8SdjjkZ58UnrsMenoUXtd//7Sz38uXX+9XWwAf1FqAACB58dJwsuWST/7mbRxo73ct680a5b0gx9IUVHBjwjn4W0DAAisgwftz1q7XDXeHqG0VLr/fvsk340b7Xsg/d//2Tf0vuYaCg0ajz01AIDAqthLc/bZUnKyz1MHDtjFZckSe/nHP5b+8Af7osNAU1FqAACBVctJwjt22B/D3rnTPlfmhRekq682kA+ORakBAARWDScJf/ONNGaMtH+/fRuoDz+0d+QAgUSpAQAEjmVVKzV790rjx9uF5pxzpI8+kjp1MpgRjkWpAQAEzu7dUl6efROmQYNUUmJfMO/bb6VevaSPP5Y6dDAdEk5FqQEABE7FXpqBA6WEBN13j/TVV1KbNvYeGgoNgokPzgEAAqfKScILF9oX1pOkl16yz6UBgolSAwAInFN7ajyDh2naNHvV9OnS975nMBOaDUoNACAwSku9peaFjedp+3b7hOBHHjGcC80GpQYAEBjr10snTqg8ubV+9WIfSdITT1S7/h4QNJQaAEBgLF8uSdqZep6OF0TpnHOk664znAnNCqUGABAYX34pSXorN1OS9OCD3McJocXbDQAQGKf21Hx28nydeaZ05ZWG86DZodQAAJru0CFp+3ZJ0lc6T7ffLkVHG86EZodSAwBouq++kiR9rT4qik3RrbcazoNmiVIDAGi6U+fTfKlMXXIJVw6GGZQaAECTWafOp1mu83X99YbDoNmi1AAAmqasTOXL7dsjrI3P5OrBMIZSAwBomk2bFF1cqHwlqdukfmrVynQgNFeUGgBA05w69LRCwzXpCj7yBHMoNQCAJin+1D5JeLnO18SJhsOgWaPUAACapGSJvafmUM9MdexoOAyaNUoNAKDxjhxRm31bJEmdp5xnOAyaO0oNAKDRyr60P/W0Tb009vuphtOguaPUAAAa7eC79vk0q2PO19ChhsOg2aPUAAAazZ1ln09zpE+mYmIMh0GzR6kBADROWZk67LT31CRPyDQcBqDUAAAaybNmgxJLC5SvJJ1zwzmm4wCUGgBA43z32ueSpJWxIzQwg4vuwTxKDQCgUU4sskvNgV6jFMVvE4QB3oYAgIazLLXfZpeaxItHGg4D2Cg1AIAGc3+To/buvfIoRmdPHW46DiCJUgMAaITd/7T30qyPOVd9hrQ0nAawUWoAAA1WuMAuNblnjZLLZTgMcAqlBgDQYG0326UmZuwow0mASpQaAECDuPcfVdeiTZKks24cYTgNUIlSAwBokO2vfKkoWdoR3Uu9R6eZjgN4UWoAAA1y7AP70FNOOufTILxQagAADZK03i411kjOp0F4odQAAPzmzner97EVkqQzr+eiewgvlBoAgN+2zFujBLmV50pVj4m9TccBfFBqAAB+O/SOfehpZ6dRckVxQg3CC6UGAOC3xNV2qfGcx/k0CD+UGgCAX9wnytUnb6kkqfM1lBqEH0oNAMAvm1/foLY6qkJXK3W76lzTcYBqKDUAAL8cemOxJGl7h5FyxcWaDQPUgFIDAPBL4sosSdKJ88eZDQLUglIDAKhXycly9Tm0RJLU8ZqxhtMANYsxHQBwgn1r9mnr7NeU8tlbGlTwRUC3HStpckC3WN3mlsN0qMd5is4crjOmDFe38b3kiub/PKi06d+blKHDKlKiuv1gqOk4QI0oNUANykrKtHzmv3XGcw+qm2d7va/vdGqKVP2KVkrrV0rrJT3btG0djErTtp6XKfbKyzVg5gS17NAyIBlh1sE37ENP2zuM1CDOp0GY4r9iaLYObTqo9ckjJZer2hQdH6ORz9zgV6GBrw7lBzRq2//pvN9dpZZprWoc39qmL7rfqDW//1jlpeWm/xg4TYsViyVJJ84bZzQHUBdKDRzPKre0+Jzp1X6Bth+QpoEFy5q8/RVpl+uL6a+qILdAsqyAT56SEr37zjvylJQEZftVp8Nb87Tqtwv02QUPa0WHy3UwKi0AfwP+G7n7Xzr3vvGKio2utwB9G9tDS66fo+K84pBmbI5K3Jb6HLTPp+lwNefTIHxx+AmOs3L2fA2bdZl32SVpXAO38VXH76njy39Q1/H139tmeAO3Hc7a9W6ndg9cIj1wSZO3lZO1S7ueek+tP31bg49nBSCdr66lO9X1tTul1+70rqvp/KMdcX10+N7fa9jsy7msfyNtfONrnatDKlYLdb9mmOk4QK3YU4OIt/aPn/r8D75qoanLkrNvU0mBu8Y9Fufte9evQoPanTm2u8b+5y4NPrbY7z1FVlm5try6VlkDZ6gsQD+eepRs0fDffs8+8bmWvT7rkkdp54dbA/L9nOjgvxdLkrZ3GCFXfJzZMEAdKDWIOFa5pVWpl3p/IWX84qJ6v2bH+5ur/QIds+U5xbXiB3Q4cUW51Oe6wRq77i+KtsrqLUGHNuzX4rEPqUCtmvR9BxV8obMm9am19GSdM01FB4sC9KeMPAkrTl2fZhiHnhDeKDWICFa5pROuFpLLJVd0lIYe/qjW1y4e+UC1X349Lu8bwrQIlfYD0jRu8SwlWQV1nn+0Zd4arWrX+ENqYzf+rdaTnpf+6B+yyq0A/qnCS4nbUt8DiyVJHa4ZZzQLUB9KDcLa5z1u8haZFjpZ42uWdbna5xfYuM9/G+KUCHd9rs/Q0LwFdR72WnrzC43a9uhXflrjoa2lt8wN8J/CjI1vbVWaDuqEEtTtGiedQQYnotQg7OQsz/X+Yhi18+UaX7PqNx96fyGN2PPvECeE07iiXBo995ZaS8+x3ce0tMfNDdrm6Lm3VCs6m1oNj7jDWPtftw897WifKVdCvOE0QN0oNQgb75/7kORy6czMM2p8vmqRGfq/l4Y4HZqzNl1ba/T2uTUWni2vZeuQq4Nf2+lftLLaYazFFz4c1oevWny1WJJUzPk0iAARVWqWLFmiK664Qp07d5bL5dI777xjOhIC4IuEiySXS1esfbjac1kDp1NkENb6XDtI7csPVCs76/7i38fYx332kM/hq9XtxodNySlxW+p34FNJUvtrLjCcBqhfRJWaoqIiDRo0SE8//bTpKAiAQVPuUmxcnEa6P6323N4VeyXL0th1fzWQDGi6QTPGVCs6x3cfVW50lzq/bsiRj31KTta4h0KUuLpNr29Umg7a93u67nxjOQB/RVSpmThxon7729/qqquuMh0FTfBR2lTFxsWpm76t/uSpH/5nDOsc+mBAkLXu2kadS/f4FJ31zyyt82vGZj3scxXlUO7FOfT6J5KkbWljuD4NIoKjryjsdrvldru9y/n5+ZIkj8cjj8cT8O9Xsc1gbNsJPrntDV360g91+gdrv9WZ6lxy6h5LjF01vK/8F4lj1fe28+S5rcS7vO0/G9T/uiE1vrZr6U7p1N3Tj7pS1PLE/kZdJdnfcUpa8bEkqfD8CyJqTAMpEt9TpgRzrPzdpsuyrPA4eNtALpdLb7/9tqZMmVLra2bNmqXZs2dXWz9v3jwlJiYGMR2qKi0q0/d/+P1q60sUqw/fecNAIiByFP3hK93wxWN1vuaVKx5V8q39Avp9S0+UacL1NylJhXr1l39X4siOAd0+0BDFxcW64YYbdPz4cSUnJ9f6OkeXmpr21KSnpysvL6/OQWksj8ejRYsWafz48YqNjQ349iNRXtyZ6qT91dYXFRbp448ZK3/wvvKf08dq47PLlDFjXK3PZyePVv+8T+rdjj/jtOkfX2rwtLE67GqnpOK99nk+zZDT31OBFMyxys/PV2pqar2lxtGHn+Lj4xUfX/26CrGxsUF9cwZ7+5Hg28/3qOvoM9XptPX71u5Xp8Fpiju1K5Gx8h9j5T+njlXG9LHSdPv/ocvuel0j/nKdz/OD85dKcXH6ukWG+havqXd7dY3T8f/Yn97aesaFGsH1aRz7ngqGYIyVv9trcPW++eabtWTJkgYHQvOxy9VdXUef6bPug76/lCxLnQanGUoFOMuIp66VLEvlnrJqz/U9sda+qvFNzzd6+ymr7fNpSkbVf281IFw0uNQUFBRowoQJ6tWrlx599FHt3bs3GLlqVFhYqOzsbGVnZ0uSdu3apezsbOXk5IQsA2p34phbcrnUXbt9n7AsXb7590YyAU4XFRPl/STV3uh0n+dGv3yb5HI1+BNTJw8Xqc+xLyVJnX90ccCyAsHW4FLz1ltvae/evZo+fbreeOMNdevWTRMnTtSbb74Z9LPDV61apYyMDGVkZEiSZs6cqYyMDD344INB/b6o38Kb56lFSoLPuvfH/MH+YQsgJM4ozanx35wrOkprfv+x39v5+rmlipNHe6K7qtclZwUyIhBUjTrzq127drrrrru0du1arVixQj179tTUqVPVuXNn3XPPPfrmm28CnVOSNG7cOFmWVW168cUXg/L94CeXSxNe+qHPqnJPma7I+oWhQEAzZ1k6vOWQz6pz7xuvJX1/6teX579tn2y886yLG/WRccCUJp3Ovm/fPi1cuFALFy5UdHS0Jk2apE2bNqlfv37685//HKiMCGcu3x94h9VWsix7lzgAY9qdnVptr82YLf/QV52m1Pu1HTbapSZmAufTILI0+DePx+PRW2+9pcsvv1xdu3bVG2+8oXvuuUf79u3TSy+9pIULF+qVV17Rww9Xv48PnKPwYHG1QpN133y1sw4bSgSgRpalxUMr95qet/9dfX7lk7W+/NDXefaJxpJ6335hsNMBAdXgj3R36tRJ5eXluv7667VixQoNHjy42msuueQStWnTJgDxEI7W/GO1zv3pUJ91JYUlGtuSjzsC4Wjcyj9o8RUdNe4Du9xc8N979e/vvVbja7f8/TO1l7Qt4Rz1HsCnFRFZGryn5s9//rNyc3P1zDPP1FhoJCklJUW7du1qajaEof9Ofq5aoZFlKY5CA4S1ce//j7Jbj/UuX/Oz62p8XekC+9DTgf4cekLkaXCpmTp1qhISEup/IRzn/b6/1GXv/cx3JZ9uAiLG4GOLfZaXXvGEz7JVbqnHjo8kSa2u5KPciDyczQm/LE66XFdsqfwB+GXsGAoNEIFOHDnhnb/wo/t9nts+f5vOLNutk4pX39vHhTgZ0HSUGtQrOypD4wr/613+oOudyizJMpgIQGOdfj2p3YsqL8Gx94UFkqTNbUcroV3LkOYCAoFSgzotix+nwVa2d/mDC/+ky3c/Yy4QgCY7srvyU4rdJvT2zrf8wj70lD/i0pBnAgKBUoNafdLm+xpRZY/MRze+oss/ucdgIgCBkNQ5qdo697ET6n9osSSp048pNYhMlBrU6IMed+mi4//xLs+f/KwueeVGg4kABNPXzy1Vok4oN+oM9Z7Sz3QcoFEoNajmo6n/1OU7/+Jd/mD07zTpHf8urw4gMmyIH+ydLyspU8Gb9qGnbWddyq0RELEoNfCx6d+bdMk/p3qX/9vj57p8yb0GEwEIhvX/M8M7v/rRj9R5g32SsOvSS0xFApqMUgOv43sL1f/aAd7lTeqny7Y/ZTARgGBpObStdz766afU4+RmlSlK/WZwfRpELkoNvFp38T15sL+1yVASAMFW9RDTkMMLJUkbW52v9r1TTEUCmoxSA9tpN6fkwnpA83NkKIeeENkoNaDQAJAkdbyZj3IjslFqmrkPet7ts+wp9pgJAiCkilYf8Vk+7Gqns28YYigNEBiUmmbs67e36PIdlScCr3lulWJbxBhMBCBU0ub8x2f5m67jFRUbbSgNEBiUmmas71V9vfMfdrpF597G/9KA5uKivA98ll2TJhpKAgQOpaa5Ou08mom5LxgKAsC0MkXp7HsmmY4BNBmlphlanHS57wpODAaatU3JmWrTM9V0DKDJKDXNzM5Pdmlc4X+9y3lbD9fxagDNwZHMy+t/ERABKDXNzFkXn+Wdf7/fvUrt3baOVwNoDjrdRqmBM1BqmpPTzqO5YtPvDAUBYNLSHzzts9z7yv6GkgCBRalpJpY88JHvCs6jAZqtC9+b6Z3/tN907soNx6DUNBNjHq28UuhXf/zcYBIA4aTltRx6gnNQapqD0w47nTdzpKEgAMLNwBljTUcAAoZS43Cf/vwd3xUcdgKatW8/2e6z3CIlwVASIPAoNQ534V+v9M5//Z+vDSYBEA66XtzLO79k6hyDSYDAo9Q42WmHnfpe2cdQEADhqPfMy0xHAAKKUuNQOz7Z7buCw04ATtOuf0fTEYCAotQ4VI+Lu3vnP/7ZGwaTAAgXy3/1jukIQFBRahwoK9H3brsX//0HhpIACCfn/67yHLtX/9/zBpMAwUGpcRir3NLYEwsql8vKDaYBEK4Sh3ADSzgPpcZhXNGVf6VfxF/IlUIBSJJKT3hMRwCCjlLjILuzvvVZHnnyE0NJAISbqMR47/xnt71sMAkQPJQaB+k2rpt3/vOHFpkLAiDsRKnyE5Aj/nKtwSRA8FBqHOKDMb/3WR4162JDSQCEu6hoDkvDmSg1DnH50vu88yeOnDCYBEC4WTzhUe/8qhT+wwPnotQ4wDeuXj7L3MsFQFXjFj3gnR+c+6HBJEBwUWocoJeq3KCOKwcDqENMQozpCEDQUGoiXZX7O30Rf4HBIADC0bq/fWE6AhAylJoIVnqy1Gd55MlPDSUBEK4GTRvlnXcfLTaYBAg+Sk0Ei2kR651/P/PROl4JAFJ8mxamIwBBRamJUEd2HvNZvmLZr80EARC2vnlnk+kIQEhRaiJU2x4p3vms++YbTAIgXPW6coB3vuhAocEkQGhQaiLQ4e1HfZbHPj6xllcCgK1lh5amIwBBR6mJQO16tfXOf/WHJQaTAAhX333xbf0vAhyGUhNh8jbu91k+7xejDSUBEM66jOrmnT+665ixHEAoUWoiTOo5nbzzK3/HR7gB1C+lW2vTEYCQoNREkLyvD/ksD7uXi+0BqG77e5tNRwCMoNREkNR+Hbzzqx5daDAJgHDWc3J/73zhvgKDSYDQotREiJPHTvosD/31eENJAESSVh1bmY4AhAylJkIkpFReCXTZjFcNJgEQzlbM4rpVaL4oNRHAKve98/aIv1xnKAmAcDd89mXe+fKS0jpeCTgPpSYCuKIr/5qyzplmMAmASBIVG206AhBSlJoIM3b906YjAAhTWRf/xjufG93FYBLADEpNuHO5vLN7oruZywEg7I395EHvfOfSPQaTAGZQaiJIeuku0xEAAAhblJowtrTPbaYjAIgQOxL6eeez+t1hMAlgDqUmjI3e+nzlgmXV/kIAzV4P99fe+bGb/mYwCWAOpSZMbf33OtMRAESI4rxi0xGAsECpCVNnXzvYO5+3+aC5IADCXmL7lt75r/+5ymASwCxKTRgqLy33WU7t295QEgCRpu8Ph5iOABhDqQlDVS+YteT6OQaTAAh3Xz3wnukIQNig1IS5MfNuNx0BQBg779HJ3vkyN7dFQPNGqQkzKztcVv+LAKAG0XHcFgHNG6UmzAw7VOUOu3yMG0Advovt7p3P6nGLwSRAeKDUhJFdC7aajgAggnQp3e2dH7v9BXNBgDARcaXmb3/7m7p3766EhAQNGTJES5cuNR0pYLpP7OOdP7TxgMEkAMJd7vIc0xGAsBNRpeb111/X3XffrQceeEBr167V6NGjNXHiROXkOO8fd/v+HUxHABDGOmd29c7nfsXNKwEpwkrNn/70J9166636yU9+or59++rJJ59Uenq65syJ/I89H4lq551fln6twSQAIk3n4V1MRwDCQozpAP4qKSnR6tWr9atf/cpn/YQJE7Rs2bIav8btdsvtdnuX8/PzJUkej0cejyfgGSu22Zhtt7WOeOeH7XglKPnCSVPGqrlhrPzXXMZqa5uRGnBqfn3SCPVt4J+3uYxTIDBW/gvmWPm7zYgpNXl5eSorK1NaWprP+rS0NO3fv7/Gr3nsscc0e/bsausXLlyoxMTEoOSUpEWLFjXo9flLD2lqleX58+fX+lqnaehYNWeMlf+cPlaTi1d653e9cq92NfJnhtPHKZAYK/8FY6yKi/27v1nElJoKLpfLZ9myrGrrKvz617/WzJkzvcv5+flKT0/XhAkTlJycHPBsHo9HixYt0vjx4xUbG+v318VOifPOH95xSJPSWwc8W7hp7Fg1R4yV/5rDWH2XtcNnedKkSQ3eRnMYp0BhrPwXzLGqONJSn4gpNampqYqOjq62V+bgwYPV9t5UiI+PV3x8fLX1sbGxQX1zNmX77c5KDXCa8BbsvwsnYaz85+Sx6j6+r3f+wNpcpTXhz+nkcQo0xsp/wRgrf7cXMScKx8XFaciQIdV2ay1atEgjRowwlKrpDkZ39M5/3uNHBpMAiDRpgzuZjgCElYjZUyNJM2fO1NSpUzV06FBlZmbqueeeU05Ojm6/PXLvj9ShvPJ6NKO2v2QwCYCwV+VQ+7LOP1Dk/ncOCI6IKjXXXnutDh8+rIcfflj79u3TgAEDNH/+fHXt2rX+Lw5DR3ccUYrpEAAi0oi9b5iOAISdiCo1knTnnXfqzjvvNB0jIFJ6Vl6bZvfCbepmLgqAMJd14z801nQIIMxFzDk1TtdtfC/TEQCEsbH/+ql3vtxTZjAJEL4oNYYsufE50xEARIijO4/6LEfF8KMbqAn/MgwZ86+feeetsnKDSQCEu5Qebb3zX7/4lcEkQHij1IQBV1TNFw8EgNP1vWm46QhA2KLUGFDoauWdXzzifoNJAIS9Kh/j/jz9OoNBgPBHqTGglYq88+O+eMRgEgCRZFTOq6YjAGGNUhNiJ46cMB0BQIRYkXaF6QhARKHUhFiLdpV3B9/yWra5IADC3vCDH1QuWJa5IECEoNQY1OfaQaYjAAhTi2/gsg9AQ1FqQmjv8j2mIwCIEONerbzsQ+kJj8EkQOSg1ITQGZlneuePbMszmARAONv84gqf5ZiEiLujDWAEpcaQtr3a1f8iAM1Svx+f550/uG6fwSRAZKHUhMi6vy4xHQFABNi3aq/PcoeBHQ0lASIPpSZEBv288v66HB8HUJtOw7p45zc+v9xgEiDyUGoM4Pg4gJocWH/AZ3nArefV8koANaHUhMAX07kKKID6pQ2qPNSU/efPDCYBIhOlJgRGPnODd547cgOoyaGNvntpBt89zkwQIIJRakKMO3IDqEn7cyr30qz53SKDSYDIRakJspW/WWA6AoAwdzA712f53HsvNpQEiGyUmiAb9uBE7zyHngDUpEPGGd75Vb/7xGASILJRakKIQ08ATvf1v9b4LA+990JDSYDIR6kJIq4xAaA+fW8c4p3f9uZ6g0mAyEepCaIBt2V657ngHoDTLf3pyz7Lvb9/jqEkgDNQakKEC+4BON3of9zknT++87DBJIAzUGqC5EA2N6EDULtlPX/ks9y6e1tDSQDnoNQESVpGZ+/88d1HDSYBEI5G7HjFO1/uKTOYBHAOSk0ItO7axnQEAOHE5ftJyKgYfhQDgcC/pCCwyi3TEQCEKc+JUt8VFj8vgECh1ATB4cSzvPNf3fcfg0kAhJvYxFjv/BfdfmgwCeA8lJog6FS+1zt/3uNXGkwCIJys++sSn+WRu/5pKAngTJQaAAiRQT8f653/+p+rDCYBnIlSE2AFL2zyzm9LGGgwCYBwsq2F78+Dvj8cUssrATQWpSbAbnz/Ae98r6Jsc0EAhI3y0nL1PrnBZxlA4FFqgogbWAKQpKjYaO/8rtjeiormZwMQDJQaAAiiJdfP8VnuXrLVUBLA+Sg1AbTyrMqPZ35+61yDSQCEizGv3emdz/nkG4NJAOej1ATQiO/e8M6Pev5mc0EAhIfTrhx85oU9DQUBmgdKDQAEwarfLvBdwZWDgaCj1ABAEAz9fxO988vve9tgEqD5oNQEyOILZnvns370nMEkAIw77bDT+Y9PMZMDaGYoNQEybvEs7/wIzqcBmq2lP37BdwWHnYCQodQAQIBY5ZZGv/gT7/K6p5caTAM0P5QaAAgQV7Tvj9RB00YZSgI0T5QaAAiAIldL3xUcdgJCjlITAFnXPOOdf/kHfzCYBIAJm19coZYq9i4XHSg0mAZovig1ATD2jene+dY39jKYBEDIWZb6/fg87+KSYf+jlh1a1vEFAIKFUgMATRHl+2N0zIonDAUBQKkBgMY67Xo0nEcDmEWpAYBGyBp8l8+y+/hJQ0kAVKDUAEADbX9no8au+4t3ecX97yg+Od5gIgASpQYAGuTksZPqeeU53uVdsb00/JHJBhMBqECpAYAGSEhp4bPcvWSboSQATkepAQB/cWIwENYoNQDgDwoNEPYoNQBQn9MKTZm71FAQAHWh1ABAXU4rNIc2HVR0XLShMADqQqkJsMKvDpuOACBQTis0uz/ervb92hsKA6A+lJoA8BS6vfM/fOxWg0kABMxphebrV1ap20U9DIUB4A9KTQDEtowzHQFAIJ1WaNb9JUt9bxxiKAwAf1FqgmB3UobpCAAaq4Y9NINmjDEUBkBDxJgO4BiW5f1h2Mu9SVa5JVeUq54vAhBWTis0ez7brr7jOOQERAr21ATQEVdb77wrmqEFIkX+d/nVCs3R7YeVTqEBIgq/eQMoyb3fd8XpF+sCEHZWP7ZQyemtfdaVe8qU0qNtLV8BIFxRagLsjef/7buCYgOErW8SBmjI/Zf4rrQsRcXwoxGIRPzLDbC41Dh9Nfu/vispNkD4cbnUy73Jdx23PgAiGqUmCM799XitfOgD35Uul7a9ud5MIABee7J2VvuPxtJet1BoAAfg009BMmzWZTp41T51GNTJu6731YPsGX54AkYUuxKVrhM+6/Z+sVujR3Q1lAhAIFFqgqjDwI4+H/X2crnkUYxiLY+ZYEAzU3SwSC3TWinx9CcsS2eYCAQgKDj8FAqWpaVTn/NZFatSu+xwvg0QVCWuOLVMa+Wzbmnfn7LHFHCgiCk1jzzyiEaMGKHExES1adPGdJwGG/3ybbX/ED1VbjjnBgicjc8vl1wuxcl3j6in0K3Rm581lApAMEVMqSkpKdHVV1+tO+64w3SUprGsWstN76sHeQtO8aGiEAcDnKGspEyxcXEacFumz/oV7SdJlsW92gAHi5hzambPni1JevHFF80GCZRTxWbJgDs1ZtOcak8ndqjcXb5j/lb1mNg7ZNGASBUbF6eralhvlZVrOLctARwvYkpNY7jdbrndbu9yfn6+JMnj8cjjCfxJuhXbbMi2M9c+JY+eUkFugdp2a1fja3pMOts7v771aPU58HHE31eqMWPVXDFW9YuNq3nvy+o/fqKBM0ZLZaVSWYhDhTHeU/5jrPwXzLHyd5suy4qss+VefPFF3X333Tp27Fi9r501a5Z3D09V8+bNU2Jitc9BhI381cc09Tc3+/XaL5Iv0KEXfx7xJQdojMlTptS4fkGnH8g958bQhgEQNMXFxbrhhht0/PhxJScn1/o6o6WmttJR1cqVKzV06FDvckNKTU17atLT05WXl1fnoDSWx+PRokWLNH78eMXGxgZkm+7jJ9WqfcOyrnziUw3++aiAfP9gCcZYORVj5evwtsPqOKBTjc8ddaVoydtzGat68J7yH2Plv2COVX5+vlJTU+stNUYPP02fPl3XXXddna/p1q1bo7cfHx+v+Pj4autjY2OD+uYM5PZjU2N9Tixe+fCHGvbQpDq/ZtgvLpR+4bvuq3vf0nm/q+lsA7OC/XfhJM19rLJG/Fpjv3xcHWt4bm90us4ozVErj0eaP7/Zj5W/GCf/MVb+C8ZY+bs9o6UmNTVVqampJiNEnGEPTpQerCw5q3/3sYb8any9X3fe778v/b76+j2Ldyh97FmBjAgEzM6PvtFZl9onyY+t4fml3aZq9K6XuYAeAEkR9JHunJwcZWdnKycnR2VlZcrOzlZ2drYKCwtNRzNqyH0XV35M3LKk8nJ9cfYtfn99+rgelRcBrDJ9NuR/VF5aHsTkQM32rfzO+z6sKDSn2/rqGsmyNHrXyyFOByCcRUypefDBB5WRkaGHHnpIhYWFysjIUEZGhlatWmU6WnhxuTRyywu+RceytPj7f23QZi5Y8ydFxUbXWHg2J2Ro95KcIP0B0Bx9+fNXve+vTsPTa3/hqffz2ddlhC4cgIgRMaXmxRdflGVZ1aZx48aZjhYRxr05vVrRKT3h0dKzbmrwtvq5s9VtbNcaC49cLpW6YrT2oXe4DD1q9e2nO3zeM5l/vaHW1x7bfazOi1YCQIWIKTUIvJiEGI3e8WK1siPL0vb3Nsutxl15NUZlynj4SikqqtbiExsXJ+sX76tgb35g/1AIS4svedTn77/rRT3rfP3x3Ue978U2XVuHKCWASEepQY16XtFX8Za7xsJTWuTW5+f/T5O/x5TtL6ht99Rai0/V6ZOLH1PBfm4dEe5OHj2hjUmZ1f7+xi18oM6v25Q4zOc91rprm9AEBuAolBo0WExinEZ9+USNhUeWJavc0pcPfqh8JQXse170yf1K6tTKrwIkl0vHXCn6bOwsHVi3P2AZYCsrKVPWqAdqHPeEtokaULi8/m0oSiWFJd73TP+iFSFIDsDpKDUIOJdLypx9qZKt/FqLj6ekRK8/NU+Le94alAxtdEwXLJmttMGd/C5CVaeTrgR90f1GrXjgXZ04XByUjOGm8ECRPrvqr9oX3aXOsYmOj9HYLx5t0LaX3jHP5+8/2ipTXEuu+QEgsBx97yeEt4SuiRq5eY4U+3y9r923/FvtuOURjfr6HyFIJiXIrZG7/yU9+i+pYb+/m6xIiToZlagSV7w8ipXlitIgy9I+1z2SpBjLo7Zlh5Qgdz1baphWki5o4jaOuNrKs3aT0gb5XiJvdBO3CwD+oNQgInQ6v6s6bX5O0nN+f83hrXnacPcL6rPwKXUs3xe8cAHWUsVqWR6+e4e+jTlLpe/O97nRaoW2BvIAQAUOP8Gx2p2dqnEf3qeOZbm1Hgaraypzl2r9s8v02fB7tbnFuab/OEG3ZPAMfbdkZ73j0tWzo8ZCAwCmsacGqEV0XLQG/jRT+mmm0Rwej0fz58/XpEmTgnrvmTFB2zIAhAZ7agAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCPEmA4QSpZlSZLy8/ODsn2Px6Pi4mLl5+crNjY2KN/DKRgr/zFW/mOs/MM4+Y+x8l8wx6ri93bF7/HaNKtSU1BQIElKT083nAQAADRUQUGBWrduXevzLqu+2uMg5eXlys3NVVJSklwuV8C3n5+fr/T0dO3Zs0fJyckB376TMFb+Y6z8x1j5h3HyH2Plv2COlWVZKigoUOfOnRUVVfuZM81qT01UVJS6dOkS9O+TnJzMm99PjJX/GCv/MVb+YZz8x1j5L1hjVdcemgqcKAwAAByBUgMAAByBUhNA8fHxeuihhxQfH286SthjrPzHWPmPsfIP4+Q/xsp/4TBWzepEYQAA4FzsqQEAAI5AqQEAAI5AqQEAAI5AqQEAAI5AqQmC3bt369Zbb1X37t3VokUL9ejRQw899JBKSkpMRwtLjzzyiEaMGKHExES1adPGdJyw8re//U3du3dXQkKChgwZoqVLl5qOFJaWLFmiK664Qp07d5bL5dI777xjOlJYeuyxxzRs2DAlJSWpQ4cOmjJlirZu3Wo6VliaM2eOBg4c6L2QXGZmpj788EPTscLeY489JpfLpbvvvtvI96fUBMGWLVtUXl6uZ599Vps2bdKf//xn/f3vf9f9999vOlpYKikp0dVXX6077rjDdJSw8vrrr+vuu+/WAw88oLVr12r06NGaOHGicnJyTEcLO0VFRRo0aJCefvpp01HCWlZWlqZNm6bly5dr0aJFKi0t1YQJE1RUVGQ6Wtjp0qWLHn/8ca1atUqrVq3ShRdeqMmTJ2vTpk2mo4WtlStX6rnnntPAgQPNhbAQEr///e+t7t27m44R1ubOnWu1bt3adIywMXz4cOv222/3WdenTx/rV7/6laFEkUGS9fbbb5uOEREOHjxoSbKysrJMR4kIKSkp1vPPP286RlgqKCiwevXqZS1atMgaO3asdddddxnJwZ6aEDl+/Ljatm1rOgYiRElJiVavXq0JEyb4rJ8wYYKWLVtmKBWc5vjx45LEz6Z6lJWV6bXXXlNRUZEyMzNNxwlL06ZN02WXXaaLL77YaI5mdUNLU3bs2KG//vWv+uMf/2g6CiJEXl6eysrKlJaW5rM+LS1N+/fvN5QKTmJZlmbOnKlRo0ZpwIABpuOEpQ0bNigzM1MnT55Uq1at9Pbbb6tfv36mY4Wd1157TWvWrNHKlStNR+GcmoaYNWuWXC5XndOqVat8viY3N1eXXnqprr76av3kJz8xlDz0GjNWqM7lcvksW5ZVbR3QGNOnT9f69ev16quvmo4Sts4++2xlZ2dr+fLluuOOO3TTTTdp8+bNpmOFlT179uiuu+7SP//5TyUkJJiOw56ahpg+fbquu+66Ol/TrVs373xubq4uuOACZWZm6rnnngtyuvDS0LGCr9TUVEVHR1fbK3Pw4MFqe2+AhpoxY4bee+89LVmyRF26dDEdJ2zFxcWpZ8+ekqShQ4dq5cqVeuqpp/Tss88aThY+Vq9erYMHD2rIkCHedWVlZVqyZImefvppud1uRUdHhywPpaYBUlNTlZqa6tdr9+7dqwsuuEBDhgzR3LlzFRXVvHaKNWSsUF1cXJyGDBmiRYsW6corr/SuX7RokSZPnmwwGSKZZVmaMWOG3n77bS1evFjdu3c3HSmiWJYlt9ttOkZYueiii7RhwwafdT/+8Y/Vp08f3XfffSEtNBKlJihyc3M1btw4nXnmmXriiSd06NAh73MdO3Y0mCw85eTk6MiRI8rJyVFZWZmys7MlST179lSrVq3MhjNo5syZmjp1qoYOHerd25eTk6Pbb7/ddLSwU1hYqO3bt3uXd+3apezsbLVt21ZnnnmmwWThZdq0aZo3b57effddJSUlefcEtm7dWi1atDCcLrzcf//9mjhxotLT01VQUKDXXntNixcv1oIFC0xHCytJSUnVzslq2bKl2rVrZ+ZcLSOfuXK4uXPnWpJqnFDdTTfdVONYffbZZ6ajGffMM89YXbt2teLi4qxzzz2Xj97W4rPPPqvxPXTTTTeZjhZWavu5NHfuXNPRws4tt9zi/bfXvn1766KLLrIWLlxoOlZEMPmRbpdlWVYoSxQAAEAwNK8TPQAAgGNRagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagAAgCNQagBErEOHDqljx4569NFHveu++uorxcXFaeHChQaTATCBG1oCiGjz58/XlClTtGzZMvXp00cZGRm67LLL9OSTT5qOBiDEKDUAIt60adP08ccfa9iwYVq3bp1WrlyphIQE07EAhBilBkDEO3HihAYMGKA9e/Zo1apVGjhwoOlIAAzgnBoAEW/nzp3Kzc1VeXm5vv32W9NxABjCnhoAEa2kpETDhw/X4MGD1adPH/3pT3/Shg0blJaWZjoagBCj1ACIaL/85S/15ptvat26dWrVqpUuuOACJSUl6YMPPjAdDUCIcfgJQMRavHixnnzySb3yyitKTk5WVFSUXnnlFX3++eeaM2eO6XgAQow9NQAAwBHYUwMAAByBUgMAAByBUgMAAByBUgMAAByBUgMAAByBUgMAAByBUgMAAByBUgMAAByBUgMAAByBUgMAAByBUgMAABzh/wMC3jYhPC3lRgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Affichage des résultats\n",
    "plt.figure()\n",
    "plt.plot(x, y, label='phase', color=\"blue\")\n",
    "plt.plot(x1, y1, label='phase', color=\"red\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "plt.figure()\n",
    "plt.plot(t, x, label='temps', color=\"blue\")\n",
    "plt.plot(t, x1, label='temps', color=\"red\")\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5e8e5e4-64d4-4cd5-86d0-67bbf0025939",
   "metadata": {},
   "source": [
    "\n",
    "PARTIE 2: ECOULEMENT DANS LES ARTERES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "f60963c6-40de-4b49-89a3-3ab734e8ca20",
   "metadata": {},
   "outputs": [],
   "source": [
    "def flux(U):\n",
    "    A, q = U\n",
    "    if mode == 'nonlineaire':\n",
    "        return np.array([q,(q**2)/A + A*(A-1)])\n",
    "    elif mode == 'lineaire':\n",
    "        return np.array([q,A])\n",
    "# G(t) entree\n",
    "def G(t):\n",
    "    return np.array([1 + 0.2 * np.sin(10 * t),0.2 * (1.1 + np.sin(10 * t))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "fb9e2bff-7e18-4c6d-8be6-57090a19125b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# donnees \n",
    "mode = 'nonlineaire'  # 'lineaire' ou 'nonlineaire'\n",
    "L = 2.0               \n",
    "M = 100               \n",
    "dx = L / (M + 1)     \n",
    "x = np.linspace(0, L, M + 2)  \n",
    "T = 4.2               \n",
    "dt = 0.013 #013 if mode == 'nonlineaire' else 0.02   \n",
    "Nt = int(T / dt)     \n",
    "lambda_ = dt / dx     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "72ef147c-b3d2-4578-9836-e54f41f62f8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialisation de U\n",
    "U = np.zeros((2, M + 2))  \n",
    "U[0, :] = 1.0             \n",
    "U[1, :] = 0.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "0b67ef23-9f56-4482-b7a9-d4db324b4842",
   "metadata": {},
   "outputs": [],
   "source": [
    "# LAX-FRIEDRICHS\n",
    "for n in range(Nt):\n",
    "    Un = U.copy()  \n",
    "    # entree\n",
    "    U[:, 0] = G(n * dt)\n",
    "    # milieu\n",
    "    for j in range(1, M + 1):\n",
    "        f_plus = flux(Un[:, j + 1])\n",
    "        f_minus = flux(Un[:, j - 1])\n",
    "        U[:, j] = 0.5*(Un[:, j+1]+Un[:,j-1])-0.5 *lambda_ *(f_plus-f_minus)\n",
    "    f_plus = flux(Un[:, M + 1])\n",
    "    f_minus = flux(Un[:, M])\n",
    "    U[:, M + 1] = Un[:, M + 1] - lambda_ * (f_plus - f_minus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "1f1ff2db-cb86-4fe3-9297-573dd7791ca4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6565\n"
     ]
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(x, U[0], color='black', label='A')\n",
    "plt.plot(x, U[1], color='blue', label='q')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print(lambda_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44c8326c-62bc-4c13-963e-7de8cbd30d8d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab4397a4-ac2e-4cb6-a4ca-9fa4d20fdbd3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:base] *",
   "language": "python",
   "name": "conda-base-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
