隐式欧拉法的Python 实现

隐式欧拉法的Python实现如下所示：

def implicit_euler(rangee, h, fun, x0, y0):
    step = int(rangee / h)
    x = [x0 + [h * i for i in range(step)]
    u = [y0 + [0 for i in range(step)]
    v = ["null"] + [0 for i in range(step)]
    
    for i in range(step):
        v[i + 1 = u[i + h * fun(x[i], u[i])
        u[i + 1 = u[i + h/2 * (fun(x[i], u[i]) + fun(x[i], v[i + 1]))

    plt.plot(x, u, label="implicit euler")
    return u

这段代码中，我们定义了一个函数`implicit_euler`，它接受参数`rangee`表示求解的范围，`h`表示步长，`fun`表示微分方程的函数，`x0`和`y0`表示初始条件。然后我们初始化了一些变量，包括时间步长`step`，自变量`x`和因变量`u`。接下来，我们使用隐式欧拉法的迭代公式进行计算，最后使用`plt.plot`函数绘制出结果，并返回因变量的数组。<span class="em">1</span><span class="em">2</span><span class="em">3</span>
#### 引用[.reference_title]
- *1* *3* [Python数值求解微分方程(欧拉法,隐式欧拉)](https://blog.csdn.net/m0_59485658/article/details/126310098)[target="_blank" data-report-click={"spm":"1018.2226.3001.9630","extra":{"utm_source":"vip_chatgpt_common_search_pc_result","utm_medium":"distribute.pc_search_result.none-task-cask-2~all~insert_cask~default-1-null.268^v1^koosearch"}}] [.reference_item style="max-width: 50%"]
- *2* [常微分方程之欧拉法、隐式欧拉法、改进欧拉法以及梯形法的原理](https://blog.csdn.net/liuqihang11/article/details/122203027)[target="_blank" data-report-click={"spm":"1018.2226.3001.9630","extra":{"utm_source":"vip_chatgpt_common_search_pc_result","utm_medium":"distribute.pc_search_result.none-task-cask-2~all~insert_cask~default-1-null.268^v1^koosearch"}}] [.reference_item style="max-width: 50%"]
[ .reference_list ]