New Quadratic Integration

[Namir]

Thanks Dieter I made the changes that you suggested.

My own (very limited) testing shows that the new algorithm generally yields more accurate results than Simpson's Rule. Of course this advantage comes at a computational price (I used old compact Simpson code that we had discussed a few years back on this forum). So increased accuracy comes at the cost of more CPU work. Fare enough!

Here is the updated VBA code:

Quote:Function f(ByVal X As Double) As Double
f = Exp(X) - 3 * X ^ 2
End Function

Function Area(ByVal A As Double, ByVal B As Double, ByVal N As Integer)
Dim Sum As Double
Dim Blast As Double, Fa As Double, Fb As Double, Fc As Double, Fm As Double
Dim Ca As Double, Cb As Double, Cm As Double
Dim K1 As Double, K2 As Double, K3 As Double
Dim Incr As Double, m As Double, C As Double
Dim I As Integer

Blast = B
Incr = (B - A) / N
Sum = 0
For I = 1 To N
B = A + Incr
C = (A + B) / 2
Fa = f(A)
Fb = f(B)
Fc = f(C)
Fm = (Fa + Fb) / 2

m = A * ((Fm - Fc) * (Fm - Fb)) / ((Fa - Fc) * (Fa - Fb)) + _
C * ((Fm - Fa) * (Fm - Fb)) / ((Fc - Fa) * (Fc - Fb)) + _
B * ((Fm - Fa) * (Fm - Fc)) / ((Fb - Fa) * (Fb - Fc))

Fm = f(m)

Ca = Fa / (A - m) / (A - B)
Cm = Fm / (m - A) / (m - B)
Cb = Fb / (B - A) / (B - m)

K1 = (Ca + Cm + Cb)
K2 = (Ca * (m + B) + Cm * (A + B) + Cb * (m + A))
K3 = (Ca * m * B + Cm * A * B + Cb * m * A)

Sum = Sum + Incr * (K1 / 3 * (B ^ 2 + A * B + A ^ 2) - K2 / 2 * (B + A) + K3)

A = B
Next I
Area = Sum

Namir