Meine alten Sachen aus RALV

Numerische_Integration/num_int_trapezformel.py

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+def f(xi, yi):
+    ys = xi + yi
+    return ys
+
+
+# Gegeben:
+x0 = 0
+y0 = 0
+h = 0.2
+xmax = 0.4
+Ey = 0.0001
+
+x = [x0]
+y = [[y0]]
+
+n = 0
+while x[-1] < xmax:
+    x.append(x[-1]+h)
+    fn = f(x[n], y[n][-1])
+    if n == 0:
+        y_neu = y[n][-1] + h * fn
+    else:
+        y_neu = y[n-1][-1] + 2*h * fn
+    y.append([y_neu])
+    dy = 1
+    while dy > Ey:
+        y_neu = y[n][-1] + h/2 * (fn + f(x[n+1], y[n+1][-1]))
+        y[-1].append(y_neu)
+        dy = abs(y[-1][-2]-y[-1][-1])
+    n += 1
+
+print(x)
+print(y)
+
+werte = []
+for i in range(len(x)):
+    werte.append((x[i], y[i][-1]))
+
+for paar in werte:
+    print(f"({round(paar[0], 5)}, {round(paar[1], 5)})")
+
+integral = 0
+for i in range(len(werte)-1):
+    integral += (werte[i+1][1]+werte[i][1])/2 * (werte[i+1][0]-werte[i][0])
+
+print(f"Integral = {round(integral, 5)}")