向前欧拉的python代码实现

向前欧拉方法是一种数值解微分方程的简单算法，用于估计连续时间系统的离散状态。以下是一个基本的Python实现，假设我们有一个一阶常微分方程dy/dt = f(t, y)，初始条件为y0：

import numpy as np

def forward_euler(f, tspan, y0, step_size):
    """
    Forward Euler method implementation

    Parameters:
    f (function): The derivative function dy/dt = f(t, y)
    tspan (tuple): Start and end time of the integration (t0, tf)
    y0 (float or array): Initial value of y
    step_size (float): Size of each time step

    Returns:
    times (numpy array): Array of time points
    ys (numpy array): Array of estimated values for y at each time step
    """
    t0, tf = tspan
    n_steps = int((tf - t0) / step_size) + 1
    times = np.linspace(t0, tf, n_steps)
    ys = np.zeros_like(times)

    # Set the first value
    ys = y0

    # Apply the forward Euler method
    for i in range(1, len(times)):
        ys[i] = ys[i-1] + f(times[i-1], ys[i-1]) * step_size

    return times, ys

# Example usage
def example_derivative(t, y):
    # Replace this with your actual derivative function
    return 1.0

tspan = (0, 10)
y0 = 0
step_size = 0.1
times, ys = forward_euler(example_derivative, tspan, y0, step_size)

在这个例子中，`f(t, y)`是你需要提供的函数，表示dy/dt。`forward_euler`函数会根据给定的时间范围、初始值和步长计算出y值序列。