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add: TP1/2

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Arthur Danjou
2025-03-24 16:07:17 +01:00
parent f41866ea2f
commit e1ec07b5c7
2 changed files with 47 additions and 56 deletions
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75
M1/Numerical Methods/TP1.ipynb
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@@ -170,8 +170,8 @@
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@@ -185,85 +185,85 @@
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"def euler_explicit_sir(N, T, u0, f, args):\n",
"def euler_explicit_sir(N, T, y0, f, args):\n",
" t = np.linspace(0, T, N + 1)\n",
" y = np.zeros((N + 1, len(y0)))\n",
" y[0] = y0\n",
" h = T / N\n",
" for i in range(N):\n",
" y[i + 1] = y[i] + h * F(y[i], t[i], *args)\n",
" y[i + 1] = y[i] + h * f(y[i], t[i], *args)\n",
" return t, y"
],
"id": "a32f0facb958a1a0",
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"source": [
"def heun_sir(N, T, u0, f, args):\n",
"def heun_sir(N, T, y0, f, args):\n",
" t = np.linspace(0, T, N + 1)\n",
" y = np.zeros((N + 1, len(y0)))\n",
" y[0] = y0\n",
" h = T / N\n",
" for i in range(N):\n",
" k1 = h * F(y[i], t[i], *args)\n",
" k2 = h * F(y[i] + k1, t[i + 1], *args)\n",
" k1 = h * f(y[i], t[i], *args)\n",
" k2 = h * f(y[i] + k1, t[i + 1], *args)\n",
" y[i + 1] = y[i] + 0.5 * (k1 + k2)\n",
" return t, y"
],
"id": "ca061c36b09f7200",
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"execution_count": 43
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"source": [
"def runge_kutta_order_4_sir(N, T, u0, f, args):\n",
"def runge_kutta_order_4_sir(N, T, y0, f, args):\n",
" t = np.linspace(0, T, N + 1)\n",
" y = np.zeros((N + 1, len(y0)))\n",
" y[0] = y0\n",
" h = T / N\n",
" for i in range(N):\n",
" k1 = h * F(y[i], t[i], *args)\n",
" k2 = h * F(y[i] + 0.5 * k1, t[i] + 0.5 * h, *args)\n",
" k3 = h * F(y[i] + 0.5 * k2, t[i] + 0.5 * h, *args)\n",
" k4 = h * F(y[i] + k3, t[i + 1], *args)\n",
" k1 = h * f(y[i], t[i], *args)\n",
" k2 = h * f(y[i] + 0.5 * k1, t[i] + 0.5 * h, *args)\n",
" k3 = h * f(y[i] + 0.5 * k2, t[i] + 0.5 * h, *args)\n",
" k4 = h * f(y[i] + k3, t[i + 1], *args)\n",
" y[i + 1] = y[i] + (k1 + 2 * k2 + 2 * k3 + k4) / 6\n",
" return t, y"
],
"id": "afc8571b14a6b464",
"outputs": [],
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"execution_count": 44
},
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@@ -298,13 +298,13 @@
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@@ -356,7 +356,7 @@
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@@ -389,8 +389,8 @@
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@@ -444,20 +444,7 @@
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