{"type":"rich","version":"1.0","title":"Euler's method in Python","html":"<pre class=\"wb-embed wb-embed-code\" data-lexer=\"python\">def euler(f, x0, y0, h, n):\n    \"\"\"Advance y' = f(x, y), y(x0) = y0 by n Euler steps of size h.\"\"\"\n    xs, ys = [x0], [y0]\n    x, y = x0, y0\n    for _ in range(n):\n        y = y + h * f(x, y)\n        x = x + h\n        xs.append(x)\n        ys.append(y)\n    return xs, ys\n\n# y' = y, y(0) = 1, ten steps of h = 0.1 on [0, 1]; exact value e\nxs, ys = euler(lambda x, y: y, 0.0, 1.0, 0.1, 10)\nprint(ys[-1])  # 2.5937424601... versus e = 2.718281828...</pre>","width":640,"height":320}