怎么把二分迭代法解微分方程的迭代过程打印出来python

您可以使用以下代码将迭代过程打印出来：

import numpy as np

def bisection_iter(f, a, b, N):
    """
    Solves f(x) = 0 on the interval [a,b] using N iterations of bisection method.
    Returns a list of the intermediate bisection values.
    """
    p = []  # list to store intermediate bisection values
    for n in range(1, N+1):
        c = (a + b)/2.0  # midpoint
        p.append(c)
        if f(c) == 0:
            return p
        elif f(c)*f(a) < 0:
            b = c
        else:
            a = c
    return p

def solve_differential_equation(f, x0, y0, x_range, N):
    """
    Solves the differential equation y' = f(x,y) with initial condition y(x0) = y0
    on the interval x_range = [x0, x1] using N iterations of bisection method.
    Returns a list of tuples (x, y) representing the approximation of the solution.
    """
    h = (x_range[1] - x_range[0])/float(N)
    x = x0
    y = y0
    solution = [(x, y)]
    for i in range(N):
        p = bisection_iter(lambda z: z - y - h*f(x+h,z), y, y+h*f(x,y), 10)
        y = p[-1]
        x = x + h
        solution.append((x, y))
    return solution

# example usage
f = lambda x, y: x - y  # differential equation y' = x - y
solution = solve_differential_equation(f, 0, 1, [0, 1], 10)
for x, y in solution:
    print("x = {:.3f}, y = {:.3f}".format(x, y))

这里的函数 `solve_differential_equation` 使用二分迭代法来计算微分方程的解，其中参数 `f` 是微分方程的右侧，即 $y'(x) = f(x,y(x))$。将解的近似值存储在一个列表中返回，而函数 `bisection_iter` 是一个二分迭代法的实现，用于计算微分方程的每个步骤。