Created using Colab

Author: GeoCalcul

CentralDifferenceMethod.ipynb

@@ -0,0 +1,67 @@
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+        "<a href=\"https://colab.research.google.com/github/GEORMC/Nnumerical_Methods_Course/blob/main/CentralDifferenceMethod.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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+      "outputs": [],
+      "source": [
+        "import numpy as np\n",
+        "\n",
+        "# System parameters\n",
+        "m = 1.0      # mass in kg\n",
+        "c = 0.1      # damping coefficient in Ns/m\n",
+        "k = 2.0      # stiffness in N/m\n",
+        "F = 1.0      # external force in N (constant)\n",
+        "dt = 0.1     # time step in seconds\n",
+        "t_max = 1.0  # maximum time in seconds\n",
+        "\n",
+        "# Time steps\n",
+        "n_steps = int(t_max / dt) + 1\n",
+        "\n",
+        "# Initial conditions\n",
+        "u = np.zeros(n_steps)      # displacement array\n",
+        "u[1] = 0.5 * F / m * dt**2 # initial displacement using approximation\n",
+        "\n",
+        "# Central Difference Method\n",
+        "for n in range(1, n_steps - 1):\n",
+        "    # Apply the central difference formula\n",
+        "    u[n + 1] = (F - c * (u[n] - u[n - 1]) / (2 * dt) - k * u[n]) / m * dt**2 + 2 * u[n] - u[n - 1]\n",
+        "\n",
+        "# Display results\n",
+        "time = np.arange(0, t_max + dt, dt)\n",
+        "result = np.column_stack((time, u))\n",
+        "\n"
+      ]
+    }
+  ]
+}