{ "cells": [ { "cell_type": "markdown", "id": "49e3f9ef", "metadata": {}, "source": [ "# Adaptive Runge-Kutta Method\n", "**강좌**: *수치해석*" ] }, { "cell_type": "markdown", "id": "9e9d3762", "metadata": {}, "source": [ "# Adaptive Runge Kutta Method\n", "- 2개의 정확도를 갖는 Runge Kutta 기법을 비교해서 상대 오차를 계산함\n", " - $\\tilde{y}_{n+1}$ 는 더 정확한 기법\n", " - $y_{n}$ 의 오차 : $Error \\approx | y_{n+1} - \\tilde{y}_{n+1} |$\n", " \n", " \n", "- 시간 간격 $h$ 조절 \n", " - $y_{n}$ LTE는 $Error = O(h^{p+1})$ 이다.\n", " - $y_{n}$ LTE를 $\\epsilon$ 까지 줄이려면 $h_{opt} = h (\\frac{\\epsilon}{Error})^{1/(p+1)}$\n", " * $\\epsilon = O(h_{opt}^{p+1})$ 이다.\n", "\n", "## Explicit Euler and Heun's method\n", "Explicit Euler 기법의 시간 간격을 조절하기 위해서 고차 기법으로 2차 Runge-Kutta 기법중 하나인 Heun's 기법을 사용하자. \n", "\n", "- Heun's 기법을 구하는 과정에서 Explicit Euler 기법이 첫번째 Stage에서 바로 계산이 된다.\n", "\n", "- Extended butcher tableau\n", "\n", " $$\n", " \\begin{array}{c|cc}\n", " 0 & 0 & \\\\\n", " 1 & 1 & 0 \\\\ \\hline\n", " & 1/2 & 1/2 \\\\\n", " & 1 & 0\n", " \\end{array}\n", " $$\n", " \n", "- 시간간격은 다음과 같이 조절한다.\n", " * $\\tilde{y}_{n+1}$: Huen's 기법\n", " * $y_{n+1}$: Euler Explicit 기법\n", " * $LTE \\approx | y_{n+1} - \\tilde{y}_{n+1} | = O(h^2)$\n", " * 목표 LTE: $\\epsilon = atol + rtol \\times |y|$\n", " * 최적 시간 간격: $h_{opt} = s_{fac} h (\\frac{\\epsilon}{Error})^{1/2}$\n", " * $s_{fac} = 0.9$\n", "\n", "## Embeded Runge Kutta Method\n", "- 기존 Stage에 일부 Stage를 추가해서 정확도가 다른 Runge Kutta Approximation을 동시에 계산함\n", "- Runge-Kutta-Fehlberg method, DOPRI method 등이 존재함\n", "- 여러 기법들이 존재함\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "2d53b50b", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "\n", "import numpy as np\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.dpi'] = 150" ] }, { "cell_type": "code", "execution_count": 2, "id": "62fb958d", "metadata": {}, "outputs": [], "source": [ "# 주요 상수\n", "m, c, g = 68.1, 12.5, 9.81\n", "\n", "# 우변 함수 작성\n", "def f(t, v):\n", " return g - c/m*v" ] }, { "cell_type": "code", "execution_count": 3, "id": "190509db", "metadata": {}, "outputs": [], "source": [ "# 엄밀해 계산 함수\n", "def exact(t):\n", " return g*m/c*(1-np.exp(-(c/m)*t))" ] }, { "cell_type": "code", "execution_count": 4, "id": "34ea7725", "metadata": {}, "outputs": [], "source": [ "# 시간간격\n", "h = 2.0\n", "\n", "# 최종 시간\n", "te = 30\n", "\n", "# Tolerance\n", "atol, rtol = 1e-3, 1e-3\n", "sfac = 0.9\n", "\n", "# 초기조건\n", "v0 = 0\n", "\n", "# 계신 시간 간격\n", "t = []\n", "y = []\n", "\n", "t.append(0)\n", "y.append(v0)\n", "ti, yi = 0, v0\n", "\n", "while ti < te:\n", " # Explicit Euler\n", " yn = yi + h*f(ti, yi)\n", "\n", " # Heun's method\n", " yp = yi + 0.5*h*(f(ti, yi) + f(ti, yn))\n", "\n", " # error\n", " err = yn - yp\n", "\n", " # tolerance\n", " tol = atol + rtol*np.maximum(abs(yn), abs(yi))\n", " en = np.linalg.norm(err/tol)\n", "\n", " if en < 1.0:\n", " yi = yn\n", " ti += h\n", " y.append(yi)\n", " t.append(ti)\n", "\n", " ratio = sfac*en**(-0.5)\n", " h *= ratio\n", " \n", "t = np.array(t)\n", "y = np.array(y)" ] }, { "cell_type": "code", "execution_count": 5, "id": "2c434142", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Velocity of Paratrooper')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot Exact solution and Numerical solution\n", "plt.plot(t, exact(t))\n", "plt.plot(t, y, marker='x',)\n", "\n", "# 그래프 선 이름\n", "plt.legend(['Exact', 'Adpative'])\n", "\n", "# x,y 축 이름\n", "plt.xlabel('Time (s)')\n", "plt.ylabel('Velocity (m/s)')\n", "\n", "# 그래프 이름\n", "plt.title('Velocity of Paratrooper')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }