diff --git a/main.ipynb b/main.ipynb index 820d969..5c1e084 100644 --- a/main.ipynb +++ b/main.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -10,29 +10,29 @@ "output_type": "stream", "text": [ "\n", - "Решение для уравнения a:\n", + "Solution for equation 1a:\n", "\n", - "Метод RK2:\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", - "Метод RK4:\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", - "Решение для уравнения b:\n", + "Solution for equation 1b:\n", "\n", - "Метод RK2:\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", - "Метод RK4:\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", @@ -41,7 +41,37 @@ }, { "data": { - "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "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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", 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" ] @@ -54,16 +84,16 @@ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", + "# ===================== First Task Functions ===================== #\n", "\n", - "\n", - "# Определяем функции для уравнений\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", - "# Реализация метода Рунге-Кутты 2-го порядка\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", @@ -74,7 +104,7 @@ " y[k+1] = y[k] + h * (k1 + k2) / 2\n", " return x, y\n", "\n", - "# Реализация метода Рунге-Кутты 4-го порядка\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", @@ -87,69 +117,136 @@ " y[k+1] = y[k] + h * (k1 + 2*k2 + 2*k3 + k4) / 6\n", " return x, y\n", "\n", - "# Начальные условия и параметры\n", - "equations = {\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} # Обратное интегрирование\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': runge_kutta_2,\n", - " 'RK4': runge_kutta_4\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 = [10, 20, 100, 200, 1000]\n", + "N_values = [int((2 - 1)/h) for h in h_values] # For the first task with x from 1 to 2\n", "\n", - "for eq_label, eq_params in equations.items():\n", - " print(f\"\\nРешение для уравнения {eq_label}:\")\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", - " x0 = eq_params['x0']\n", - " y0 = eq_params['y0']\n", - " x_end = eq_params['x_end']\n", - " if x_end < x0:\n", - " direction = -1\n", - " else:\n", - " direction = 1\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", - " for method_label, method_func in methods.items():\n", - " print(f\"\\nМетод {method_label}:\")\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", - " ys = {}\n", - " xs = {}\n", - " abs_errors = []\n", - " max_abs_errors = []\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 h, N in zip(h_values, N_values):\n", - " h = direction * h # Учёт направления интегрирования\n", - " x, y = method_func(eq_params['func'], x0, y0, h, N)\n", - " xs[N] = x\n", - " ys[N] = y\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", - " for i in range(1, len(N_values)):\n", - " N_prev = N_values[i-1]\n", - " N_curr = N_values[i]\n", + " ys = {}\n", + " xs = {}\n", + " abs_errors = []\n", + " max_abs_errors = []\n", "\n", - " # Поиск общих индексов для сравнения\n", - " factor = N_curr // N_prev\n", - " indices = [int(k * factor) for k in [1, N_prev]]\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", - " # Вычисление относительных ошибок\n", - " rel_errors = np.abs(ys[N_curr][indices] - ys[N_prev][[1, N_prev]])\n", - " print(f\"N_{N_curr}: {' '.join(map(str, rel_errors))}\")\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", - " # Вычисление максимальных абсолютных ошибок\n", - " max_error = np.max(rel_errors)\n", - " max_abs_errors.append(max_error)\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", - " # Построение графика логарифма абсолютных ошибок\n", - " plt.plot(np.log2(N_values[1:]), np.log2(max_abs_errors), label=f\"{method_label} для уравнения {eq_label}\")\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", - "plt.xlabel(\"log2(N)\")\n", - "plt.ylabel(\"log2(max абсолютная ошибка)\")\n", - "plt.legend()\n", - "plt.title(\"График логарифма абсолютных ошибок\")\n", - "plt.show()" + " # 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(np.log2(N_values_task[1:]), np.log2(max_abs_errors), label=f\"{method_label} for equation {task_label}{eq_label}\")\n", + "\n", + " plt.xlabel(\"log2(N)\")\n", + " plt.ylabel(\"log2(max absolute 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" ] } ],