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Runge-Kutta/main.ipynb
T

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{
"cells": [
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Solution for equation 1a:\n",
"\n",
"Method RK2:\n",
"N_20: 0.0002785283564428198 0.0038035441958399474\n",
"N_100: 4.479515251887278e-05 0.0012767268215512217\n",
"N_200: 2.7750003539495083e-07 4.103739219374347e-05\n",
"N_1000: 4.440127909788316e-08 1.3191150621594261e-05\n",
"\n",
"Method RK4:\n",
"N_20: 2.9636773035690567e-07 3.9579403434686355e-06\n",
"N_100: 9.184862648226044e-09 2.6419341025984977e-07\n",
"N_200: 2.6076918402395677e-12 3.9756997693984886e-10\n",
"N_1000: 8.526512829121202e-14 2.646061147970613e-11\n",
"\n",
"Solution for equation 1b:\n",
"\n",
"Method RK2:\n",
"N_20: 0.0014339682258658337 0.019603229003013034\n",
"N_100: 9.465097127459021e-05 0.0035429668461870456\n",
"N_200: 5.85138142383812e-08 6.395910166601126e-05\n",
"N_1000: 2.542437982366863e-08 1.8243564207320873e-05\n",
"\n",
"Method RK4:\n",
"N_20: 1.6409863435429273e-05 1.5852614062783488e-05\n",
"N_100: 5.942575315165399e-07 2.292905823431113e-06\n",
"N_200: 1.8908408172535474e-10 3.99405974960132e-09\n",
"N_1000: 6.314393452555578e-12 2.6547564146994773e-10\n"
]
},
{
"data": {
"image/png": 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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: 6.247396158842733e-06 0.0006487724632973091\n",
"N_100: 4.999227261395789e-07 0.00021289741698327092\n",
"N_200: 6.249973958510902e-10 6.760371213720973e-06\n",
"N_1000: 4.999992173765344e-11 2.169024081455362e-06\n",
"\n",
"Method RK4:\n",
"N_20: 1.778789573969597e-09 1.0195093080866968e-07\n",
"N_100: 3.0951276264179484e-11 6.3144536266435125e-09\n",
"N_200: 1.9359513991901167e-15 8.852918398360998e-12\n",
"N_1000: 3.382710778154774e-17 5.822009541134321e-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",
"\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",
" # Find common indices for comparison\n",
" factor = N_curr // N_prev\n",
" indices_prev = [1, N_prev]\n",
" indices_curr = [k * factor for k in indices_prev]\n",
"\n",
" # Compute relative errors\n",
" rel_errors = np.abs(ys[N_curr][indices_curr] - ys[N_prev][indices_prev])\n",
" print(f\"N_{N_curr}: {' '.join(map(str, rel_errors))}\")\n",
"\n",
" # Compute maximum absolute errors\n",
" max_error = np.max(rel_errors)\n",
" max_abs_errors.append(max_error)\n",
"\n",
" # Plotting log2 of absolute errors\n",
" plt.plot(N_values_task[1:], np.log2(max_abs_errors), label=f\"{method_label} for equation {task_label}{eq_label}\")\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",
"# ===================== Solve First Task ===================== #\n",
"solve_task('1', equations_first, N_values, x0_task=None, x_end_task=None)\n",
"\n",
"# ===================== Solve 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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