From 0db8d58d8f985a3cedb16c0343233d807d64f8d3 Mon Sep 17 00:00:00 2001
From: Namu <namulabre@gmail.com>
Date: Mon, 19 Jan 2026 10:33:51 +0100
Subject: [PATCH] Feat: Ajoute les fonctions de calcul d'equa diff

---
 tp8.py | 87 ++++++++++++++++++++++++++++++++++++++++++++++++++++------
 1 file changed, 78 insertions(+), 9 deletions(-)

diff --git a/tp8.py b/tp8.py
index 7188770..e65062f 100644
--- a/tp8.py
+++ b/tp8.py
@@ -1,24 +1,93 @@
 import matplotlib.pyplot as plt
 
 
-def euler(f, n: int, delta_x: float, x_0: float, y_0: float) -> list[float]:
-    results = []
+def euler(f, n: int, h: float, x_0: float, y_0: float) -> tuple[list[float], list[float]]:
+    """
 
+    :param f: la fonction f (ou y)
+    :param n: jusqu'où va le calcul (le nombre d'itérations)
+    :param h: le pas de chaque itération
+    :param x_0: dans la condition initiale, c'est la valeur passée en entrée de f
+    :param y_0: dans la condition initiale, c'est la valeur de sortie de f.
+    :return:
+    """
+    results_x = [x_0]
+    results_y = [y_0]
+    # h c'est delta_x
     x = x_0
     y = y_0
     for i in range(n):
-        x = x + delta_x
-        y = y + delta_x * f(x, y)
-        results.append(y)
+        if i < 4:
+            x = x + h
+            y = y + h * f(x, y)
+        else:
+            h = .3
+            x = x + h
+            y = y + h * f(x, y)
+        results_x.append(x)
+        results_y.append(y)
 
-    return results
+    return results_x, results_y
+
+
+def runge_kutta(f, n: int, h: float, x_0: float, y_0: float) -> tuple[list[float], list[float]]:
+    results_x = [x_0]
+    results_y = [y_0]
+    x = x_0
+    y = y_0
+    for i in range(n):
+        if i < 4:
+            k_1 = f(x, y)
+            k_2 = f(x + (h / 2), y + (h / 2) * k_1)
+            x = x + h
+            y = y + h * k_2
+        else:
+            h = .3
+            k_1 = f(x, y)
+            k_2 = f(x + (h / 2), y + (h / 2) * k_1)
+            x = x + h
+            y = y + h * k_2
+        results_x.append(x)
+        results_y.append(y)
+
+    return results_x, results_y
+
+
+def taylor(f, f_derive_x, f_derive_y, n: int, h: float, x_0: float, y_0: float) -> tuple[list[float], list[float]]:
+    results_x = [x_0]
+    results_y = [y_0]
+
+    x = x_0
+    y = y_0
+
+    for i in range(n):
+        if i < 4:
+            x = x + h
+            y = y + h * f(x, y) + (h ** 2) / 2 * (f_derive_x(x, y) + f_derive_y(x, y) * f(x, y))
+        else:
+            h = .3
+            x = x + h
+            y = y + h * f(x, y) + (h ** 2) / 2 * (f_derive_x(x, y) + f_derive_y(x, y) * f(x, y))
+        results_x.append(x)
+        results_y.append(y)
+
+    return results_x, results_y
 
 
 def exercice1() -> None:
     f = lambda x, y: -2 * x * y + 1
-    results = euler(f, n=20, x_0=0, y_0=1, delta_x=.2)
-    plt.plot(results)
-    plt.title('Euler')
+    f_derive_x = lambda x, y: -2 * y + 1
+    f_derive_y = lambda x, y: -2 * x + 1
+
+    results_x_euler, results_y_euler = euler(f, n=5, x_0=0, y_0=1, h=.2)
+    results_x_runge, results_y_runge = runge_kutta(f, n=5, x_0=0, y_0=1, h=.2)
+    results_x_taylor, results_y_taylor = taylor(f, f_derive_x, f_derive_y, 5, x_0=0, y_0=1, h=.2)
+
+    plt.plot(results_x_euler, results_y_euler, color='green')
+    plt.plot(results_x_runge, results_y_runge, color='red')
+    plt.plot(results_x_taylor, results_y_taylor, color='blue')
+
+    plt.title('La giga fonction pour les equations différentielles. (mieux que le sex garanti 3 ans)')
     plt.show()