Numerical integration: Difference between revisions

Content added Content deleted

Inline

@@ Line 165: / Line 165: @@
       Sum : Scalar := F(A) + F(B);
       X   : Scalar := 1.0;
    begin
       while X <= Scalar (N) - 1.0 loop
          Sum := Sum + 2.0 * F (A + X * (B - A) / Scalar (N));
@@ Line 175: / Line 175: @@
    function Simpsons (A, B : Scalar; N : Positive) return Scalar is
       H     : constant Scalar := (B - A) / Scalar (N);
-      Sum_1 : Scalar := 0.0;
+      Sum_U : Scalar := 0.0;
-      Sum_2 : Scalar := 0.0;
+      Sum_E : Scalar := 0.0;
    begin
-      for I in 0 .. N - 1 loop
+      for I in 1 .. N - 1 loop
-         Sum_1 := Sum_1 + F (A + H * Scalar (I) + 0.5 * H);
+         if I mod 2 /= 0 then
-         Sum_2 := Sum_2 + F (A + H * Scalar (I));
+            Sum_U := Sum_U + F (A + H * Scalar (I));
+         else
+            Sum_E := Sum_E + F (A + H * Scalar (I));
+         end if;
       end loop;
-      return H / 6.0 * (F (A) + F (B) + 4.0 * Sum_1 + 2.0 * Sum_2);
+      return (H / 3.0) * (F (A) + F (B) + 4.0 * Sum_U + 2.0 * Sum_E);
    end Simpsons;
 end Integrate;</lang>