euler method

euler_method.ipynb

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    {
      "cell_type": "code",
      "source": "#Numerical Solutions to 1st-Order ODE via Euler's Method\n#Importing External Libraries\nimport numpy as np\nfrom matplotlib import pyplot as plt\nimport math\n\nfrom ipywidgets import interactive, fixed",
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      "execution_count": 5,
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      "cell_type": "code",
      "source": "def euler_method(init_t = 0., init_y = 0., final_t = 0., steps = 1):\n    #Step size\n    deltat = (final_t - init_t) / steps\n    #Define t-values\n    x = np.linspace(init_t, final_t, steps+1)\n\n    #Initializing array for the slope (dy/dt = m) and y-values\n    m = np.zeros([steps+1])\n    y = np.zeros([steps+1])\n    #For loop for the updated y-value\n    y[0] = init_y\n    for i in range(1,steps+1):\n        m[i-1] = y[i-1] ** 2 - 4 * x[i-1] #dy/dt = your choice (right now, it's t*y)\n        y[i] = y[i-1] + m[i-1] * deltat #y_new = y_old + (slope)*(step size)\n    print()\n    #Printing the data\n    t = \"t\"\n    Y = \"y\"\n    slope = \"f(t,y)\"\n    print(f\"{t : ^17}\", f\"{Y : ^12}\", f\"{slope : ^12}\")\n    print(\"--------------------------------------------\")\n    for i in range (steps+1):\n        print(f\"{round(x[i],4) : >10}\",\" | \" , f\"{round(y[i],4) : >10}\", \" | \" , \n    f\"{round(m[i],4) : >10}\")\n        print(\"--------------------------------------------\")\n\n    #Plotting the solution\n    plt.plot(x,y, linestyle='-', marker='o')\n    plt.locator_params(axis=\"x\", nbins = steps + 1)\n    plt.grid(color = 'green', linestyle = '--', linewidth = 0.2)\n    plt.xlabel(\"t\")\n    plt.ylabel(\"y(t)\")\n    plt.title(\"Approximate solution with Euler's Method\")\n    plt.show()",
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      "execution_count": 10,
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    {
      "cell_type": "code",
      "source": "w=interactive(euler_method, steps=(0, 10, 1))\nw",
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      "execution_count": 13,
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          "data": {
            "text/plain": "interactive(children=(FloatSlider(value=0.0, description='init_t', max=1.0), FloatSlider(value=0.0, descriptio…",
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requirements.txt

ipywidgets==7.7.0
matplotlib==3.5.1
numpy==1.18.4