第四章1

120-3.py

@@ -0,0 +1,27 @@
+x1, x2 = 3, 6
+
+
+def fx(x):
+    return x/(4+x**2)
+
+# n等分，x1到x2的区间，type=1表示梯形法，type=2表示辛普森法
+def CompositeNewtonCotes(n, type):
+    if type == 1:
+        h = (x2 - x1) / n
+        result = 0
+        for i in range(n):
+            result += (fx(x1 + i * h) + fx(x1 + (i + 1) * h))
+        result *= (h / 2)
+        return result
+    elif type == 2:
+        h = (x2 - x1) / n
+        result = -fx(x1) + fx(x2)
+        for i in range(n):
+            result += (4 * fx(x1 + (i + 0.5) * h) + 2 * fx(x1 + i * h))
+        result *= (h / 6)
+        return result
+    
+
+if __name__ == "__main__":
+    print("Composite Trapezoidal Rule: ", CompositeNewtonCotes(8, 1))
+    print("Composite Simpson's Rule: ", CompositeNewtonCotes(4, 2))