q11

120-5.py

@@ -2,12 +2,16 @@ import math
 
 def fx(x):
     if x == 0:
-        x = 1e-10  # Avoid division by zero
-    return math.sin(x)/x
+        x = 1e-10  # Avoid division by zero  #如果x能为0，注释掉这行##############
+        pass
+    return math.sin(x)/x   #把函数改成题干的形式###################
 
 # 龙贝格方法 积分
 def Romberg(a, b, err):
+    table = [[],[],[],[]]
     t00 = (b-a)*(fx(a)+fx(b))/2
+    table[0].append(t00)
+    print(f"t0(0)={t00}")
     t01 = t10 = t11 = t20 = t21 = t30 = t31 = 0
     k = 1
     while True:
@@ -15,34 +19,49 @@ def Romberg(a, b, err):
         for i in range(1, 2**(k-1)+1):
             tmp += fx(a + (b-a)*(2*i-1)/(2**k))
         t01 = t00/2+(b-a)*tmp/(2**k)
+        print(f"t0({k})={t01}")
+        table[0].append(t01)
         
         if k>1:
             t11 = (4*t01-t00)/3
-            
+            print(f"t1({k-1})={t11}")
+            table[1].append(t11)
             if k>2:
                 t21 = (16*t11-t10)/15
-                
+                print(f"t2({k-2})={t21}")
+                table[2].append(t21)
                 if k>3:
                     t31 = (64*t21-t20)/63
+                    print(f"t3({k-3})={t31}")
+                    table[3].append(t31)
                     if abs(t31-t30) < err:
                         break
                     t30 = t31
                 else:
                     t30 = (64*t21-t20)/63
+                    print(f"t3(0)={t30}")
+                    table[3].append(t30)
                 t20 = t21
             else:
                 t20 = (16*t11-t10)/15
+                print(f"t2(0)={t20}")
+                table[2].append(t20)
             t10 = t11
         else:
             t10 = (4*t01-t00)/3
+            print(f"t1(0)={t10}")
+            table[1].append(t10)
         t00 = t01
         k += 1
+    print("Romberg table:")
+    for i in range(len(table)):
+        print(f"t{i}: {table[i]}")
     return t31, k
 
-
+# 把范围ab与精度换成题干的############
 if __name__ == "__main__":
     a = 0
     b = 1
-    err = 0.5e-6
+    err = 0.5e-6    #把精度要求改成题干的##################
     result, k = Romberg(a, b, err)
     print(f"Result: {result}, k={k}")