python中平流方程的四阶Runge-Kutta程序设计

import numpy as np

def runge_kutta(f, x0, t0, tf, dt):
    t = np.arange(t0, tf, dt)
    x = np.zeros_like(t)
    x[0] = x0

    for i in range(1, len(t)):
        k1 = f(t[i-1], x[i-1])
        k2 = f(t[i-1] + dt/2, x[i-1] + dt/2 * k1)
        k3 = f(t[i-1] + dt/2, x[i-1] + dt/2 * k2)
        k4 = f(t[i-1] + dt, x[i-1] + dt * k3)
        x[i] = x[i-1] + dt/6 * (k1 + 2*k2 + 2*k3 + k4)

    return t, x

# 定义平流方程
def convection(t, x):
    return -0.5 * x

# 设置初始条件和求解参数
x0 = 1.0
t0 = 0.0
tf = 10.0
dt = 0.1

# 调用四阶Runge-Kutta方法求解平流方程
t, x = runge_kutta(convection, x0, t0, tf, dt)

# 打印结果
for i in range(len(t)):
    print("t = {:.1f}, x = {:.4f}".format(t[i], x[i]))