Runge-Kutta 是常用的高精度求解 ODE 初值问题的数值方法, 尤其是 RK4。本文的目的在于展示一个 python 代码,允许输入自定义的 Butcher tableau 来进行RK方法选择,为后续数值算法的性质介绍提供方便。Butcher tableau 中的矩阵 A 决定了数值方法是否是显性或隐性。显式方法的优点在于更新方便,计算量小,但是对于刚性问...
(x, y): ff = 0.1*x/y**2 - 0.95 return ff def newtonMethod(assum, d1, d3): y = assum Next = 0 A = F(d1, y, d3) B = ff(d1, y) if F(d1, y, d3) == 0.0: return y else: Next = y - A / B if abs(A - F(d1, Next, d3)) < 1e-5: return Next '...
2,1)plt.plot(t_values,y_values,label='RK4 Approximation',color='blue')plt.title('Runge-Kutta Method Result')plt.xlabel('Time (t)')plt.ylabel('Value (y)')plt.legend()# 绘制饼状图,展示数值解的分布plt.subplot(1,2,2)plt.pie(y_values,labels=[f't={t:.2f}'fortint_values],autopc...
4. 测试函数 现在,我们可以调用runge_kutta函数并打印结果: # 设置参数x0=0# 起始 x 值y0=1# 起始 y 值x_end=2# 结束 x 值h=0.1# 步幅# 调用龙格-库塔法results=runge_kutta(f,x0,y0,x_end,h)# 输出结果forx,yinresults:print(f"x:{x:.1f}, y:{y:.4f}") 1. 2. 3. 4. 5. 6. ...
在Python中使用4阶Runge-Kutta方法求解方程组是一种常见的数值计算方法,用于求解常微分方程组。该方法通过逐步逼近解的方式,将方程组离散化为一系列的步骤来计算。 具体步骤如下: 1. ...
为了使用4阶Runge-Kutta方法求解y(1),我们需要遵循以下步骤: 定义4阶Runge-Kutta方法的计算公式: 4阶Runge-Kutta方法通过以下步骤来计算微分方程的近似解: text k1 = h * f(x_n, y_n) k2 = h * f(x_n + h/2, y_n + k1/2) k3 = h * f(x_n + h/2, y_n + k2/2) k4 = h *...
虽然数学家基于他们的专业知识和对世界的理解来创建模型，而机器学习算法以某种隐蔽的不完全理解的方式描述...
Runge-Kutta Method in Python and MATLAB 2 - 3 hrs278 learners You Will Learn How To Recognize the role of differential equations in modeling... Generate custom implementations of numerical methods for... Apply the Runge-Kutta Method to numerically s...Read More ...
The follow set of scripts calculate the response of a specific single-degree-of-freedom system to an arbitrary base input time history, via the Runge-Kutta fourth order method. The scripts also demonstrate the passing of numpy arrays to the function, which processes the the data and then retur...
(2021). RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method. Expert Systems with Applications, 181, 115079. J JA - Jaya Algorithm OriginalJA: Rao, R. (2016). Jaya: A simple and new optimization algorithm for solving constrained and unconstrained ...