Contributor: DAVID PINCH
{ This simple Pascal program computes a definite integral using Simpson's
approximation. Efficiency has been sacrificed for clarity, so it should
be easy to follow the logic of the program. - DJP }
Var { Declare variables }
a : Integer; { Left point }
b : Integer; { Right point }
d : Real; { Delta x }
i : Integer; { Iteration }
n : Integer; { No. of intervals }
SubTotal : Real;
Function y(x:real):Real; { Define your function here }
Begin
y:=1/x
End;
Function Coefficient(i:Integer):Integer;
Begin
If (i=0) or (i=n) Then
Coefficient:=1
Else
Coefficient:=(i Mod 2)*2+2
{ Notes:
The MOD operater returns the remainder of a division. This allows
us to determine if the partition is odd or even.
MOD 2 = 0
MOD 2 = 1
An examination of the coefficients of a typical approximation sum shows
an interesting pattern: Odd partitions have 4 as a coefficient and even
partitions have 2 as a coefficient. The first and last partitions are
exceptions to this rule. This pattern is used as a basis for
calculating the coefficient of a given partition. }
End;
Function xi(i:Integer):Real;
Begin
xi:=a+i*d
End;
Begin
a:=1;
b:=2;
Repeat
Write('Subintervals? ');
ReadLn(n);
Until (n Mod 2)=0; { Even number required }
d:=(b-1)/n;
WriteLn;
WriteLn(' n xi f(xi) c cf(xi)');
WriteLn('-------------------------------');
For i:=0 to n Do
Begin
WriteLn(i:3, xi(i):8:3, y(xi(i)):8:3, Coefficient(i):4,
Coefficient(i)*y(xi(i)):8:3);
SubTotal:=SubTotal+Coefficient(i)*y(xi(i))
End;
WriteLn;
WriteLn('SubTotal',SubTotal:23:3);
WriteLn('Result = ', (d/3)*SubTotal:0:50)
End.
{ Quick Optimizations:
a. Remove the WriteLn statement in the For loop.
b. Turn on 80x87 support.
c. Consolidate some of the procedures.
peace/dp }