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2024-11-22 13:41:38 +03:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Solution for equation 1a:\n",
"\n",
"Method RK2:\n",
"N_20:\n",
"0.0002785283564 0.0006147262836 0.001008931808 0.001453439014 0.001930378282 0.002412818397 0.002869546941 0.003270516965 0.003589271118 0.003803544196\n",
"N_100:\n",
"9.442991941e-05 0.0002090095219 0.0003440780151 0.0004970853173 0.000661623814 0.0008275460164 0.000982606614 0.001114948045 0.001215060742 0.001276726822\n",
"N_200:\n",
"3.056533167e-06 6.776709096e-06 1.117548006e-05 1.617051613e-05 2.154595543e-05 2.695219014e-05 3.196167493e-05 3.616337836e-05 3.92460027e-05 4.103739219e-05\n",
"N_1000:\n",
"9.836686345e-07 2.181501333e-06 3.598507423e-06 5.208179537e-06 6.94057232e-06 8.682048339e-06 1.029342858e-05 1.164114701e-05 1.262499773e-05 1.319115062e-05\n",
"\n",
"Method RK4:\n",
"N_20:\n",
"2.963677304e-07 7.195955476e-07 1.286779597e-06 1.981418709e-06 2.730011495e-06 3.402355173e-06 3.863917016e-06 4.06174507e-06 4.057771658e-06 3.957940343e-06\n",
"N_100:\n",
"2.028602708e-08 4.911409945e-08 8.745490021e-08 1.338870206e-07 1.831774981e-07 2.266869501e-07 2.56161016e-07 2.690227525e-07 2.696008536e-07 2.641934103e-07\n",
"N_200:\n",
"3.11146664e-11 7.517186873e-11 1.334505839e-10 2.034639124e-10 2.769553475e-10 3.409823535e-10 3.83870713e-10 4.027747025e-10 4.044338198e-10 3.975699769e-10\n",
"N_1000:\n",
"2.071232075e-12 5.012879001e-12 8.885336911e-12 1.354294454e-11 1.841016228e-11 2.266986598e-11 2.55298005e-11 2.677325028e-11 2.689759526e-11 2.646061148e-11\n",
"\n",
"Solution for equation 1b:\n",
"\n",
"Method RK2:\n",
"N_20:\n",
"0.001433968226 0.002966446899 0.004500158049 0.006118077901 0.007943671725 0.01011452626 0.01276400597 0.01593449952 0.01917439382 0.019603229\n",
"N_100:\n",
"0.0002544574831 0.0006490274359 0.001083585901 0.001555473082 0.002087532901 0.002708169175 0.003435162915 0.004225851337 0.004773274812 0.003542966846\n",
"N_200:\n",
"4.989075659e-06 1.577579261e-05 2.841768018e-05 4.243009511e-05 5.827699515e-05 7.659969145e-05 9.754117317e-05 0.0001187768894 0.0001276600829 6.395910167e-05\n",
"N_1000:\n",
"1.465472705e-06 4.844589588e-06 8.845072874e-06 1.329479324e-05 1.833103302e-05 2.414770351e-05 3.077111962e-05 3.740934404e-05 3.986381442e-05 1.824356421e-05\n",
"\n",
"Method RK4:\n",
"N_20:\n",
"1.640986344e-05 1.927399391e-05 1.896334616e-05 1.858634685e-05 1.928175228e-05 2.168188937e-05 2.624829711e-05 3.257189624e-05 3.426085818e-05 1.585261406e-05\n",
"N_100:\n",
"8.782501411e-07 1.029525818e-06 9.941156065e-07 9.473647006e-07 9.576468701e-07 1.064105619e-06 1.294298038e-06 1.614401477e-06 1.566632217e-06 2.292905823e-06\n",
"N_200:\n",
"1.090825874e-09 1.270972577e-09 1.199204319e-09 1.104448866e-09 1.081153056e-09 1.186212129e-09 1.462583832e-09 1.869790101e-09 1.756605084e-09 3.99405975e-09\n",
"N_1000:\n",
"7.065736884e-11 8.222408865e-11 7.727574136e-11 7.075251496e-11 6.887024284e-11 7.540712499e-11 9.326694972e-11 1.199462751e-10 1.128612759e-10 2.654756415e-10\n"
]
},
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Solution for equation 2:\n",
"\n",
"Method RK2:\n",
"N_20:\n",
"6.247396159e-06 2.487878023e-05 5.565768745e-05 9.842805737e-05 0.0001533006145 0.000220811222 0.0003020454697 0.0003987265304 0.0005132652519 0.0006487724633\n",
"N_100:\n",
"1.997366387e-06 7.95941899e-06 1.783245443e-05 3.160261921e-05 4.935410358e-05 7.131823078e-05 9.791179558e-05 0.0001297638108 0.0001677303501 0.000212897417\n",
"N_200:\n",
"6.24108064e-08 2.488453061e-07 5.580570304e-07 9.90315554e-07 1.549198012e-06 2.243093594e-06 3.08637305e-06 4.100198781e-06 5.312965976e-06 6.760371214e-06\n",
"N_1000:\n",
"1.99718817e-08 7.963985801e-08 1.786277719e-07 3.170586584e-07 4.961266403e-07 7.185768469e-07 9.890781877e-07 1.314481255e-06 1.703958302e-06 2.169024081e-06\n",
"\n",
"Method RK4:\n",
"N_20:\n",
"1.778789574e-09 4.842148099e-09 7.349121756e-09 7.663824464e-09 4.391501718e-09 3.636483226e-09 1.741321887e-08 3.782447944e-08 6.571693723e-08 1.019509308e-07\n",
"N_100:\n",
"1.05174397e-10 3.19153648e-10 5.187487662e-10 5.928556535e-10 4.445525059e-10 1.001532191e-11 8.449324573e-10 2.1288179e-09 3.928984693e-09 6.314453627e-09\n",
"N_200:\n",
"1.59774971e-13 5.087319455e-13 8.605893775e-13 1.045441511e-12 9.127143485e-13 3.29625216e-13 8.243405958e-13 2.663091969e-12 5.300426764e-12 8.852918398e-12\n",
"N_1000:\n",
"1.076916334e-14 3.433364704e-14 5.845324225e-14 7.138734048e-14 6.32827124e-14 2.553512957e-14 5.051514762e-14 1.717515019e-13 3.466116283e-13 5.822009541e-13\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# ===================== First Task Functions ===================== #\n",
"\n",
"# Equations for the first task\n",
"def func_a(x, y):\n",
" return x + np.cos(y)\n",
"\n",
"def func_b(x, y):\n",
" return x**2 + y**2\n",
"\n",
"# Runge-Kutta 2nd order method for first-order ODE\n",
"def runge_kutta_2(f, x0, y0, h, N):\n",
" x = x0 + np.arange(N+1) * h\n",
" y = np.zeros(N+1)\n",
" y[0] = y0\n",
" for k in range(N):\n",
" k1 = f(x[k], y[k])\n",
" k2 = f(x[k] + h, y[k] + h * k1)\n",
" y[k+1] = y[k] + h * (k1 + k2) / 2\n",
" return x, y\n",
"\n",
"# Runge-Kutta 4th order method for first-order ODE\n",
"def runge_kutta_4(f, x0, y0, h, N):\n",
" x = x0 + np.arange(N+1) * h\n",
" y = np.zeros(N+1)\n",
" y[0] = y0\n",
" for k in range(N):\n",
" k1 = f(x[k], y[k])\n",
" k2 = f(x[k] + h/2, y[k] + h * k1 / 2)\n",
" k3 = f(x[k] + h/2, y[k] + h * k2 / 2)\n",
" k4 = f(x[k] + h, y[k] + h * k3)\n",
" y[k+1] = y[k] + h * (k1 + 2*k2 + 2*k3 + k4) / 6\n",
" return x, y\n",
"\n",
"# ===================== Second Task Functions ===================== #\n",
"\n",
"# Converts second-order ODE to a system of first-order ODEs\n",
"def second_order_to_system(x, y, dy):\n",
" return dy, y * np.sin(x)\n",
"\n",
"# Runge-Kutta 2nd order method for second-order ODE\n",
"def runge_kutta_2_second_order(f, x0, y0, dy0, h, N):\n",
" x = x0 + np.arange(N+1) * h\n",
" y = np.zeros(N+1)\n",
" dy = np.zeros(N+1)\n",
" y[0] = y0\n",
" dy[0] = dy0\n",
" for k in range(N):\n",
" k1_y, k1_dy = f(x[k], y[k], dy[k])\n",
" k2_y, k2_dy = f(x[k] + h, y[k] + h * k1_y, dy[k] + h * k1_dy)\n",
" y[k+1] = y[k] + h * (k1_y + k2_y) / 2\n",
" dy[k+1] = dy[k] + h * (k1_dy + k2_dy) / 2\n",
" return x, y\n",
"\n",
"# Runge-Kutta 4th order method for second-order ODE\n",
"def runge_kutta_4_second_order(f, x0, y0, dy0, h, N):\n",
" x = x0 + np.arange(N+1) * h\n",
" y = np.zeros(N+1)\n",
" dy = np.zeros(N+1)\n",
" y[0] = y0\n",
" dy[0] = dy0\n",
" for k in range(N):\n",
" k1_y, k1_dy = f(x[k], y[k], dy[k])\n",
" k2_y, k2_dy = f(x[k] + h/2, y[k] + h * k1_y / 2, dy[k] + h * k1_dy / 2)\n",
" k3_y, k3_dy = f(x[k] + h/2, y[k] + h * k2_y / 2, dy[k] + h * k2_dy / 2)\n",
" k4_y, k4_dy = f(x[k] + h, y[k] + h * k3_y, dy[k] + h * k3_dy)\n",
" y[k+1] = y[k] + h * (k1_y + 2*k2_y + 2*k3_y + k4_y) / 6\n",
" dy[k+1] = dy[k] + h * (k1_dy + 2*k2_dy + 2*k3_dy + k4_dy) / 6\n",
" return x, y\n",
"\n",
"# ===================== Main Code for Both Tasks ===================== #\n",
"\n",
"# Parameters for both tasks\n",
"methods = {\n",
" 'RK2': {'first_order': runge_kutta_2, 'second_order': runge_kutta_2_second_order},\n",
" 'RK4': {'first_order': runge_kutta_4, 'second_order': runge_kutta_4_second_order}\n",
"}\n",
"\n",
"h_values = [0.1, 0.05, 0.01, 0.005, 0.001]\n",
"N_values = [int((2 - 1)/h) for h in h_values] # For the first task with x from 1 to 2\n",
"\n",
"# First Task Equations\n",
"equations_first = {\n",
" 'a': {'func': func_a, 'x0': 1.0, 'y0': 30.0, 'x_end': 2.0},\n",
" 'b': {'func': func_b, 'x0': 2.0, 'y0': 1.0, 'x_end': 1.0} # Reverse integration\n",
"}\n",
"\n",
"# Second Task Parameters\n",
"x0_second = 0.0\n",
"y0_second = 0.0\n",
"dy0_second = 1.0\n",
"x_end_second = 1.0\n",
"N_values_second = [int((x_end_second - x0_second)/h) for h in h_values]\n",
"legend_abbreviation = \"EMSH64D04\"\n",
"\n",
"# Function to perform calculations and plotting for a given task\n",
"def solve_task(task_label, equations, N_values_task, x0_task, x_end_task, is_second_order=False):\n",
" for eq_label, eq_params in equations.items():\n",
" print(f\"\\nSolution for equation {task_label}{eq_label}:\")\n",
"\n",
" x0 = eq_params['x0']\n",
" y0 = eq_params['y0']\n",
" if is_second_order:\n",
" dy0 = eq_params['dy0']\n",
" x_end = eq_params['x_end']\n",
" if x_end < x0:\n",
" direction = -1\n",
" else:\n",
" direction = 1\n",
"\n",
" for method_label, method_funcs in methods.items():\n",
" method_func = method_funcs['second_order'] if is_second_order else method_funcs['first_order']\n",
" print(f\"\\nMethod {method_label}:\")\n",
"\n",
" ys = {}\n",
" xs = {}\n",
" abs_errors = []\n",
" max_abs_errors = []\n",
"\n",
" for h, N in zip(h_values, N_values_task):\n",
" h = direction * h # Account for integration direction\n",
" if is_second_order:\n",
" x, y = method_func(second_order_to_system, x0, y0, dy0, h, N)\n",
" else:\n",
" x, y = method_func(eq_params['func'], x0, y0, h, N)\n",
" xs[N] = x\n",
" ys[N] = y\n",
"\n",
" for i in range(1, len(N_values_task)):\n",
" N_prev = N_values_task[i-1]\n",
" N_curr = N_values_task[i]\n",
"\n",
" indices_prev = np.linspace(0, N_prev, 11, endpoint=True, dtype=int)\n",
" indices_curr = np.linspace(0, N_curr, 11, endpoint=True, dtype=int)\n",
" \n",
" rel_errors = np.abs(ys[N_curr][indices_curr] - ys[N_prev][indices_prev])\n",
"\n",
" rel_errors_without_zero = rel_errors[1:]\n",
"\n",
" if len(rel_errors_without_zero) != 10:\n",
" raise ValueError(f\"The resulting error array does not contain exactly 10 values (found {len(rel_errors_without_zero)}).\")\n",
"\n",
" print(f\"N_{N_curr}:\")\n",
" print(\" \".join(f\"{val:.10g}\" for val in rel_errors_without_zero))\n",
"\n",
" # Compute maximum absolute errors\n",
" max_error = np.max(rel_errors)\n",
" max_abs_errors.append(max_error)\n",
"\n",
" # Plotting absolute errors\n",
" plt.plot(N_values_task[1:], np.log2(max_abs_errors), label=f\"{method_label} for equation {task_label}{eq_label} ({legend_abbreviation})\")\n",
"\n",
"\n",
" plt.xlabel(\"N\")\n",
" plt.ylabel(\"Log_2 of maximum error\")\n",
" plt.legend()\n",
" plt.title(f\"Logarithm of absolute errors for task {task_label}\")\n",
" plt.show()\n",
"\n",
"# ===================== First Task ===================== #\n",
"solve_task('1', equations_first, N_values, x0_task=None, x_end_task=None)\n",
"\n",
"# ===================== Second Task ===================== #\n",
"\n",
"# Second Task Equation\n",
"equations_second = {\n",
" '': {'dy0': dy0_second, 'x0': x0_second, 'y0': y0_second, 'x_end': x_end_second}\n",
"}\n",
"\n",
"solve_task('2', equations_second, N_values_second, x0_task=x0_second, x_end_task=x_end_second, is_second_order=True)\n"
]
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