MSSC_3D_FILE_IMPORTED.ipynb

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      "cell_type": "markdown",
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        "<a href=\"https://colab.research.google.com/github/phmouras/Critical-Phenomena-in-gravitational-collapse-via-spectral-methods/blob/main/MSSC_3D_FILE_IMPORTED.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "\n",
        "\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "\n",
        "N = 30                                                   # Truncation ordem\n",
        "\n",
        "L0 = 2\n",
        "\n",
        "\n",
        "\n",
        "#r = open(\"rcol_30_L02.txt\",\"r\")   # Physical collocation points\n",
        "#initial_r = eval(r.read())\n",
        "#r.close()\n",
        "\n",
        "r = np.loadtxt(\"rcol_30_L02.txt\", dtype = \"float\")\n",
        "\n",
        "\n",
        "SB = np.zeros([N+3,N+1])\n",
        "rSB = np.zeros([N+3,N+1])\n",
        "rrSB = np.zeros([N+3,N+1])\n",
        "\n",
        "for i in range(N+1+1+1):\n",
        "  SB[i,] = np.sin((2*i+1)*np.arctan(L0/r))\n",
        "\n",
        "for i in range(N+1+1+1):\n",
        "  rSB[i,] = -np.cos((2*i+1)*np.arctan(L0/r))*(2*i+1)*L0/(r**2*(1+L0**2/r**2))\n",
        "\n",
        "for i in range(N+1+1+1):\n",
        "  rrSB[i,] = -np.sin((2*i+1)*np.arctan(L0/r))*(2*i+1)**2*L0**2/(r**4*(1+L0**2/r**2)**2)+2*np.cos((2*i+1)*np.arctan(L0/r))*(2*i+1)*L0/(r**3*(1+L0**2/r**2))-2*np.cos((2*i+1)*np.arctan(L0/r))*(2*i+1)*L0**3/(r**5*(1+L0**2/r**2)**2)\n",
        "\n",
        "psi = SB[0:N+1,:]        # Base function\n",
        "rpsi = rSB[0:N+1,:]\n",
        "rrpsi = rrSB[0:N+1,:]\n",
        "\n",
        "inv_psi = np.linalg.inv(psi)\n",
        "\n",
        "# Plot data:\n",
        "\n",
        "M = 1000       # plot truncation\n",
        "\n",
        "rplot = np.linspace(0.000001,15,M)\n",
        "\n",
        "SBplot = np.zeros([N+1,M])\n",
        "for i in range(N+1):\n",
        "  SBplot[i,] = np.sin((2*i+1)*np.arctan(L0/rplot))\n",
        "\n",
        "psiplot = SBplot[0:(N+1),:]\n",
        "\n",
        "\n",
        "\n",
        "# Base function for Krr:\n",
        "\n",
        "SB1 = 1/2*(SB[1:(N+2),:] + SB[0:(N+1),:])          # VERIFICADO\n",
        "rSB1 = 1/2*(rSB[1:(N+2),:] + rSB[0:(N+1),:])\n",
        "\n",
        "# Base function for Beta:\n",
        "SB2 = np.zeros([N+1,N+1])\n",
        "rSB2 = np.zeros([N+1,N+1])\n",
        "\n",
        "for i in range(N+1):                                                   # VERIFICADO\n",
        "  SB2[i,] = np.sin((2*(i+1/2)+1)*np.arctan(L0/r))\n",
        "\n",
        "for i in range(N+1):\n",
        "  rSB2[i,] = -np.cos((2*i+2)*np.arctan(L0/r))*(2*i+2)*L0/(r**2*(1+L0**2/r**2))\n",
        "\n",
        "# QUADRATURE INTEGRATION\n",
        "\n",
        "\n",
        "Nq = int(3/2*N)                          # Quadrature truncation\n",
        "\n",
        "gauss_quadrature = np.polynomial.legendre.leggauss(Nq + 1)\n",
        "\n",
        "new_col = gauss_quadrature[0]            # Legendre quadrature points\n",
        "\n",
        "\n",
        "# Legendre Polinomials\n",
        "\n",
        "P = np.zeros([Nq+3,Nq+1])\n",
        "colP = np.zeros([Nq+3,Nq+1])\n",
        "\n",
        "P[0,] = 1\n",
        "P[1,] = new_col\n",
        "\n",
        "colP[0,] = 0\n",
        "colP[1,] = 1\n",
        "\n",
        "for i in range(2,Nq+3):\n",
        "  P[i,] = ((2*i-1)*new_col*P[i-1,] - (i-1)*P[i-2,])/(i)\n",
        "\n",
        "for i in range(2,Nq+3):\n",
        "  colP[i,] = i*P[i-1] + new_col*colP[i-1]\n",
        "\n",
        "P_max = P[Nq+1]\n",
        "\n",
        "colP_max = colP[Nq+1]\n",
        "\n",
        "wq_col = 2/((1-new_col**2)*colP_max**2)\n",
        "\n",
        "rq = L0*(1+new_col)/(1-new_col)\n",
        "\n",
        "qSB = np.zeros([Nq+3,Nq+1])\n",
        "qrSB = np.zeros([Nq+3,Nq+1])\n",
        "qrrSB = np.zeros([Nq+3,Nq+1])\n",
        "\n",
        "for i in range(Nq+1+1+1):\n",
        "  qSB[i,] = np.sin((2*i+1)*np.arctan(L0/rq))\n",
        "\n",
        "for i in range(Nq+1+1+1):\n",
        "  qrSB[i,] = -np.cos((2*i+1)*np.arctan(L0/rq))*(2*i+1)*L0/(rq**2*(1+L0**2/rq**2))\n",
        "\n",
        "for i in range(Nq+1+1+1):\n",
        "  qrrSB[i,] = -np.sin((2*i+1)*np.arctan(L0/rq))*(2*i+1)**2*L0**2/(rq**4*(1+L0**2/rq**2)**2)+2*np.cos((2*i+1)*np.arctan(L0/rq))*(2*i+1)*L0/(rq**3*(1+L0**2/rq**2))-2*np.cos((2*i+1)*np.arctan(L0/rq))*(2*i+1)*L0**3/(rq**5*(1+L0**2/rq**2)**2)\n",
        "\n",
        "\n",
        "qpsi = qSB[0:N+1,:]\n",
        "rqpsi = qrSB[0:N+1,:]\n",
        "rrqpsi = qrrSB[0:N+1,:]\n",
        "\n",
        "# Base function for Krr in rq:\n",
        "\n",
        "qSB1 = 1/2*(qSB[1:(N+2),:] + qSB[0:(N+1),:])\n",
        "\n",
        "# Initial Conditions phi, pi and phi\n",
        "\n",
        "a0 = np.loadtxt(\"a0_30_L02.txt\", dtype = \"float\")\n",
        "\n",
        "c0 = np.loadtxt(\"c0_30_L02.txt\", dtype = \"float\")\n",
        "\n",
        "Phi = np.dot(a0, psi)\n",
        "rPhi = np.dot(a0, rpsi)\n",
        "rrPhi = np.dot(a0, rrpsi)\n",
        "\n",
        "Pi_0 = np.zeros(N+1)\n",
        "b0 = np.dot(Pi_0, psi)\n",
        "Pi = np.dot(b0, psi)\n",
        "\n",
        "Chi=np.dot(c0,psi)\n",
        "rChi=np.dot(c0,rpsi)\n",
        "rrChi=np.dot(c0,rrpsi)\n",
        "\n",
        "Chi\n"
      ],
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        "id": "HZ5Ilg9RBb13",
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      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.00456651, 0.00913695, 0.01373194, 0.01837516, 0.02309087,\n",
              "       0.02790501, 0.03284555, 0.03794308, 0.04322614, 0.048587  ,\n",
              "       0.05333811, 0.05659495, 0.05860723, 0.06031923, 0.06211351,\n",
              "       0.06377342, 0.06503881, 0.06585611, 0.06631879, 0.06655453,\n",
              "       0.06666442, 0.06671185, 0.06673082, 0.06673791, 0.06674031,\n",
              "       0.0667411 , 0.06674128, 0.06674137, 0.06674134, 0.0667414 ,\n",
              "       0.06674125])"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "\n",
        "# Runge Kutta 4th order\n",
        "\n",
        "h = 0.001   # step size\n",
        "tf = 7\n",
        "\n",
        "It = int(tf/h)\n",
        "\n",
        "t = np.linspace(0, tf, It)\n",
        "\n",
        "phi_set = np.zeros([It,M])\n",
        "chi_set = np.zeros([It,M])\n",
        "pi_set = np.zeros([It,M])\n",
        "L2HC = np.zeros([It])\n",
        "#Alpha0_a002 = np.zeros([It])\n",
        "#Alpha0_a005 = np.zeros([It])\n",
        "#Alpha0_a007 = np.zeros([It])\n",
        "#Alpha0_a081 = np.zeros([It])\n",
        "\n",
        "\n",
        "V = 0\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "for i in range(It):\n",
        "\n",
        "  # First step\n",
        "  Phi = np.dot(a0, psi)\n",
        "  rPhi = np.dot(a0, rpsi)\n",
        "  rrPhi = np.dot(a0, rrpsi)\n",
        "  Pi = np.dot(b0, psi)\n",
        "  rPi= np.dot(b0, rpsi)\n",
        "  Chi = np.dot(c0, psi)\n",
        "  rChi = np.dot(c0, rpsi)\n",
        "  rrChi = np.dot(c0, rrpsi)\n",
        "  Matrix_Krr = 2*rChi*SB1 + rSB1 + 3/r*SB1\n",
        "  inv_matrix_krr = np.linalg.inv(Matrix_Krr)\n",
        "  rhsk = - Pi*rPhi*np.exp(4*Chi)\n",
        "  ck0 = np.dot(rhsk, inv_matrix_krr)\n",
        "  Krr = np.dot(ck0, SB1)\n",
        "  rKrr = np.dot(ck0, rSB1)\n",
        "  Matrix_Alpha = rrpsi + 2*(1/r + rChi)*rpsi - 3/2*np.exp(-4*Chi)*Krr**2*psi - np.exp(4*Chi)*(Pi**2 - V)*psi\n",
        "  inv_matrix_alpha = np.linalg.inv(Matrix_Alpha)\n",
        "  rhsal = 3/2*np.exp(-4*Chi)*Krr**2 + np.exp(4*Chi)*(Pi**2-V)\n",
        "  al0 = np.dot(rhsal, inv_matrix_alpha)\n",
        "  Alpha = 1 + np.dot(al0, psi)\n",
        "  rAlpha = np.dot(al0, rpsi)\n",
        "  rrAlpha = np.dot(al0, rrpsi)\n",
        "  Matrix_Beta = rSB2/r - SB2/r**2\n",
        "  inv_matrix_beta = np.linalg.inv(Matrix_Beta)\n",
        "  rhsbe = 3/2*Alpha*np.exp(-4*Chi)*Krr/r\n",
        "  be0 = np.dot(rhsbe , inv_matrix_beta)\n",
        "  Beta = np.dot(be0, SB2)\n",
        "  rBeta = np.dot(be0, rSB2)\n",
        "  db = np.dot(Beta*rPi + np.exp(-4*Chi)*(2*Alpha/r + rAlpha + 2*rChi*Alpha)*rPhi + np.exp(-4*Chi)*Alpha*rrPhi - Alpha* V, inv_psi)\n",
        "  dc = np.dot(Beta*rChi + Beta/2/r + Alpha/4*np.exp(-4*Chi)*Krr, inv_psi)\n",
        "  da = np.dot(Alpha*Pi + Beta*rPhi, inv_psi)\n",
        "  K1 = h*(dc)\n",
        "  L1 = h*(da)\n",
        "  N1 = h*(db)\n",
        "\n",
        "  # L2-error associated to the Hamiltonian constraint\n",
        "  qPhi = np.dot(a0, qpsi)\n",
        "  rqPhi= np.dot(a0, rqpsi)\n",
        "  qPi = np.dot(b0, qpsi)\n",
        "  qChi = np.dot(c0, qpsi)\n",
        "  rqChi = np.dot(c0, rqpsi)\n",
        "  rrqChi = np.dot(c0, rrqpsi)\n",
        "  qKrr = np.dot(ck0, qSB1)\n",
        "  H = 4*rqChi**2 + 4*rrqChi + 8*rqChi/rq + 3/4*np.exp(-4*qChi)*qKrr**2 + np.exp(4*qChi)*(1/2*qPi**2 + np.exp(-4*qChi)/2*rqPhi**2)   # Hamiltonian constraint (HC)\n",
        "  L2HC[i,] = (1/2*np.dot(H**2,wq_col))**1/2     # Error L2 of HC\n",
        "\n",
        "  # Alpha in r=0\n",
        "  #Alpha0_a081[i] = 1 + np.dot(al0, psi_0)\n",
        "\n",
        "  # Second step\n",
        "  Phi = np.dot(a0 + L1/2, psi)\n",
        "  rPhi= np.dot(a0 + L1/2 , rpsi)\n",
        "  rrPhi = np.dot(a0 + L1/2, rrpsi)\n",
        "  Pi = np.dot(b0 + N1/2, psi)\n",
        "  rPi= np.dot(b0 + N1/2, rpsi)\n",
        "  Chi = np.dot(c0 + K1/2, psi)\n",
        "  rChi = np.dot(c0 + K1/2, rpsi)\n",
        "  rrChi = np.dot(c0 + K1/2, rrpsi)\n",
        "  Matrix_Krr = 2*rChi*SB1 + rSB1 + 3/r*SB1\n",
        "  inv_matrix_krr = np.linalg.inv(Matrix_Krr)\n",
        "  rhsk = - Pi*rPhi*np.exp(4*Chi)\n",
        "  ck0 = np.dot(rhsk, inv_matrix_krr)\n",
        "  Krr = np.dot(ck0, SB1)\n",
        "  rKrr = np.dot(ck0, rSB1)\n",
        "  Matrix_Alpha = rrpsi + 2*(1/r + rChi)*rpsi - 3/2*np.exp(-4*Chi)*Krr**2*psi - np.exp(4*Chi)*(Pi**2 - V)*psi\n",
        "  inv_matrix_alpha = np.linalg.inv(Matrix_Alpha)\n",
        "  rhsal = 3/2*np.exp(-4*Chi)*Krr**2 + np.exp(4*Chi)*(Pi**2-V)\n",
        "  al0 = np.dot(rhsal, inv_matrix_alpha)\n",
        "  Alpha = 1 + np.dot(al0, psi)\n",
        "  rAlpha = np.dot(al0, rpsi)\n",
        "  rrAlpha = np.dot(al0, rrpsi)\n",
        "  Matrix_Beta = rSB2/r - SB2/r**2\n",
        "  inv_matrix_beta = np.linalg.inv(Matrix_Beta)\n",
        "  rhsbe = 3/2*Alpha*np.exp(-4*Chi)*Krr/r\n",
        "  be0 = np.dot(rhsbe , inv_matrix_beta)\n",
        "  Beta = np.dot(be0, SB2)\n",
        "  rBeta = np.dot(be0, rSB2)\n",
        "  db = np.dot(Beta*rPi + np.exp(-4*Chi)*(2*Alpha/r + rAlpha + 2*rChi*Alpha)*rPhi + np.exp(-4*Chi)*Alpha*rrPhi - Alpha* V, inv_psi)\n",
        "  dc = np.dot(Beta*rChi + Beta/2/r + Alpha/4*np.exp(-4*Chi)*Krr, inv_psi)\n",
        "  da = np.dot(Alpha*Pi + Beta*rPhi, inv_psi)\n",
        "  K2 = h*(dc)\n",
        "  L2 = h*(da)\n",
        "  N2 = h*(db)\n",
        "\n",
        "  # Third step\n",
        "  Phi = np.dot(a0 + L2/2, psi)\n",
        "  rPhi = np.dot(a0 + L2/2 , rpsi)\n",
        "  rrPhi = np.dot(a0 + L2/2, rrpsi)\n",
        "  Pi = np.dot(b0 + N2/2, psi)\n",
        "  rPi= np.dot(b0 + N2/2, rpsi)\n",
        "  Chi = np.dot(c0 + K2/2, psi)\n",
        "  rChi = np.dot(c0 + K2/2, rpsi)\n",
        "  rrChi = np.dot(c0 + K2/2, rrpsi)\n",
        "  Matrix_Krr = 2*rChi*SB1 + rSB1 + 3/r*SB1\n",
        "  inv_matrix_krr = np.linalg.inv(Matrix_Krr)\n",
        "  rhsk = - Pi*rPhi*np.exp(4*Chi)\n",
        "  ck0 = np.dot(rhsk, inv_matrix_krr)\n",
        "  Krr = np.dot(ck0, SB1)\n",
        "  rKrr = np.dot(ck0, rSB1)\n",
        "  Matrix_Alpha = rrpsi + 2*(1/r + rChi)*rpsi - 3/2*np.exp(-4*Chi)*Krr**2*psi - np.exp(4*Chi)*(Pi**2 - V)*psi\n",
        "  inv_matrix_alpha = np.linalg.inv(Matrix_Alpha)\n",
        "  rhsal = 3/2*np.exp(-4*Chi)*Krr**2 + np.exp(4*Chi)*(Pi**2-V)\n",
        "  al0 = np.dot(rhsal, inv_matrix_alpha)\n",
        "  Alpha = 1 + np.dot(al0, psi)\n",
        "  rAlpha = np.dot(al0, rpsi)\n",
        "  rrAlpha = np.dot(al0, rrpsi)\n",
        "  Matrix_Beta = rSB2/r - SB2/r**2\n",
        "  inv_matrix_beta = np.linalg.inv(Matrix_Beta)\n",
        "  rhsbe = 3/2*Alpha*np.exp(-4*Chi)*Krr/r\n",
        "  be0 = np.dot(rhsbe , inv_matrix_beta)\n",
        "  Beta = np.dot(be0, SB2)\n",
        "  rBeta = np.dot(be0, rSB2)\n",
        "  db = np.dot(Beta*rPi + np.exp(-4*Chi)*(2*Alpha/r + rAlpha + 2*rChi*Alpha)*rPhi + np.exp(-4*Chi)*Alpha*rrPhi - Alpha* V, inv_psi)\n",
        "  dc = np.dot(Beta*rChi + Beta/2/r + Alpha/4*np.exp(-4*Chi)*Krr, inv_psi)\n",
        "  da = np.dot(Alpha*Pi + Beta*rPhi, inv_psi)\n",
        "  K3 = h*(dc)\n",
        "  L3 = h*(da)\n",
        "  N3 = h*(db)\n",
        "\n",
        "  # Forth step\n",
        "  Phi = np.dot(a0 + L3, psi)\n",
        "  rPhi= np.dot(a0 + L3 , rpsi)\n",
        "  rrPhi = np.dot(a0 + L3, rrpsi)\n",
        "  Pi = np.dot(b0 + N3, psi)\n",
        "  rPi= np.dot(b0 + N3, rpsi)\n",
        "  Chi = np.dot(c0 + K3, psi)\n",
        "  rChi = np.dot(c0 + K3, rpsi)\n",
        "  rrChi = np.dot(c0 + K3, rrpsi)\n",
        "  Matrix_Krr = 2*rChi*SB1 + rSB1 + 3/r*SB1\n",
        "  inv_matrix_krr = np.linalg.inv(Matrix_Krr)\n",
        "  rhsk = - Pi*rPhi*np.exp(4*Chi)\n",
        "  ck0 = np.dot(rhsk, inv_matrix_krr)\n",
        "  Krr = np.dot(ck0, SB1)\n",
        "  rKrr = np.dot(ck0, rSB1)\n",
        "  Matrix_Alpha = rrpsi + 2*(1/r + rChi)*rpsi - 3/2*np.exp(-4*Chi)*Krr**2*psi - np.exp(4*Chi)*(Pi**2 - V)*psi\n",
        "  inv_matrix_alpha = np.linalg.inv(Matrix_Alpha)\n",
        "  rhsal = 3/2*np.exp(-4*Chi)*Krr**2 + np.exp(4*Chi)*(Pi**2-V)\n",
        "  al0 = np.dot(rhsal, inv_matrix_alpha)\n",
        "  Alpha = 1 + np.dot(al0, psi)\n",
        "  rAlpha = np.dot(al0, rpsi)\n",
        "  rrAlpha = np.dot(al0, rrpsi)\n",
        "  Matrix_Beta = rSB2/r - SB2/r**2\n",
        "  inv_matrix_beta = np.linalg.inv(Matrix_Beta)\n",
        "  rhsbe = 3/2*Alpha*np.exp(-4*Chi)*Krr/r\n",
        "  be0 = np.dot(rhsbe , inv_matrix_beta)\n",
        "  Beta = np.dot(be0, SB2)\n",
        "  rBeta = np.dot(be0, rSB2)\n",
        "  db = np.dot(Beta*rPi + np.exp(-4*Chi)*(2*Alpha/r + rAlpha + 2*rChi*Alpha)*rPhi + np.exp(-4*Chi)*Alpha*rrPhi - Alpha* V, inv_psi)\n",
        "  dc = np.dot(Beta*rChi + Beta/2/r + Alpha/4*np.exp(-4*Chi)*Krr, inv_psi)\n",
        "  da = np.dot(Alpha*Pi + Beta*rPhi, inv_psi)\n",
        "  K4 = h*(dc)\n",
        "  L4 = h*(da)\n",
        "  N4 = h*(db)\n",
        "\n",
        "  # Evolution functions\n",
        "  a0 = a0 + 1/6 * (L1 + 2*L2 + 2*L3 + L4)\n",
        "  b0 = b0 + 1/6 * (N1 + 2*N2 + 2*N3 + N4)\n",
        "  c0 = c0 + 1/6 * (K1 + 2*K2 + 2*K3 + K4)\n",
        "  phi_set[i,:] = np.dot(a0, psiplot)\n",
        "  pi_set[i,:] = np.dot(b0, psiplot)\n",
        "  chi_set[i,:] = np.dot(c0, psiplot)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "J9Xlw9Pagaak"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(It):\n",
        "  plt.plot(phi_set[i,:])"
      ],
      "metadata": {
        "id": "mCY9ZaYTU0gS",
        "outputId": "53a5ae6d-2953-4015-d2c3-de50e69c7022",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot Phi Initial\n",
        "rplot = np.linspace(0.000001,10,M)\n",
        "\n",
        "plt.plot(rplot, phi_set[0,:])   #(Verificado)\n",
        "plt.xlabel('r')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "T9qACyKCRlCH",
        "outputId": "8aca04c2-9f2b-49a6-c91c-6eb2a1ea41e8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot 3D from Phi initial:\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "rplot = np.linspace(0.000001,80,M)\n",
        "\n",
        "fig = plt.figure(figsize=(12,6))\n",
        "ax1 = fig.add_subplot(121)\n",
        "ax2 = fig.add_subplot(122,projection='3d')\n",
        "\n",
        "y = phi_set[0,:]\n",
        "x = rplot\n",
        "theta = np.linspace(0, 2*np.pi, M)    # Revolution of f(phi,r)\n",
        "\n",
        "xn = np.outer(x, np.cos(theta))\n",
        "yn = np.outer(x, np.sin(theta))\n",
        "zn = np.zeros_like(xn)\n",
        "\n",
        "for i in range(len(x)):\n",
        "    zn[i,:] = np.full_like(zn[0,:], y[i])\n",
        "\n",
        "ax1.plot(x, y)\n",
        "ax2.plot_surface(xn, yn, zn)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "APTPcTUGniJ8",
        "outputId": "9c50f5c8-c630-4709-91a9-fec9c6bf0c52",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x432 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.shape(rplot)"
      ],
      "metadata": {
        "id": "upXWWCPVoRC7",
        "outputId": "cf2c8d69-d384-498a-dfa6-e639aaed36fe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(100,)"
            ]
          },
          "metadata": {},
          "execution_count": 76
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Animation plot for Phi: Scalar Field\n",
        "\n",
        "from matplotlib.animation import FuncAnimation\n",
        "from IPython.display import HTML\n",
        "\n",
        "fig = plt.figure()\n",
        "ax = plt.axes(xlim=(0, 15),ylim = (-2, 1))\n",
        "line, = ax.plot([], [], lw=2)\n",
        "\n",
        "x = rplot\n",
        "\n",
        "def init():\n",
        "    line.set_data([], [])\n",
        "    return line,\n",
        "\n",
        "def animate(i):\n",
        "  y = phi_set[i,:]\n",
        "  line.set_data(x, y)\n",
        "  return line,\n",
        "\n",
        "anim = FuncAnimation(fig, animate, init_func=init,\n",
        "                               frames=It, interval=0.1, blit=True)\n",
        "\n",
        "HTML(anim.to_html5_video())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 562
        },
        "id": "pUKW7NHEQCpD",
        "outputId": "b511f659-78b4-4d66-8d0d-a8b01b1602f6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<video width=\"432\" height=\"288\" controls autoplay loop>\n",
              "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAAQwpm1kYXQAAAKuBgX//6rcRem9\n",
              "5tlIt5Ys2CDZI+7veDI2NCAtIGNvcmUgMTUyIHIyODU0IGU5YTU5MDMgLSBILjI2NC9NUEVHLTQg\n",
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              "bWlkPTIgYl9hZGFwdD0xIGJfYmlhcz0wIGRpcmVjdD0xIHdlaWdodGI9MSBvcGVuX2dvcD0wIHdl\n",
              "aWdodHA9MiBrZXlpbnQ9MjUwIGtleWludF9taW49MjUgc2NlbmVjdXQ9NDAgaW50cmFfcmVmcmVz\n",
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              "cG1pbj0wIHFwbWF4PTY5IHFwc3RlcD00IGlwX3JhdGlvPTEuNDAgYXE9MToxLjAwAIAAAAiCZYiE\n",
              "ACf//vWxfApqyfOKDOgyLuGXJMmutiLibQDAAAADAAVQU9eBdxeICcqWdvOtvQk4jPFlQEFj2X60\n",
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              "  Your browser does not support the video tag.\n",
              "</video>"
            ]
          },
          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y"
      ],
      "metadata": {
        "id": "84viVHywhO3Z",
        "outputId": "2f63b2f6-66d9-45ad-84c1-0074fa909b9c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3.58829778e-07, 6.38697196e-07, 1.48238557e-06, ...,\n",
              "       5.47147192e-06, 5.46699702e-06, 5.46251472e-06])"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "plt.plot(t,L2HC)\n",
        "plt.yscale(\"log\")\n",
        "plt.ylabel(\"log(Error RMS)\")\n",
        "plt.xlabel(\"t\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "qR_dj-0UQDVz",
        "outputId": "6d2e5f82-e312-404a-c49c-551c6f4aa669"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 0, 't')"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}