Page 161 - Excel for Scientists and Engineers: Numerical Methods

138 EXCEL: NUMERICAL METHODS

1
b-u jF((b-a)z+(b+U) (7-1 1)
2
2
-1
and equation 7-9 becomes

(b - U)Z, + (b + U) (7-12)
2

which permits integration over any range.
The code shown in Figure 7-12 performs Gaussian quadrature using equation
7-12 and a tenth-order Legendre polynomial. Some results returned by the
function are shown in Figure 7- 13.

3ption Explicit
............................................................
Function Integrate(expression, variable, from-lower, to-upper, Optional -
tolerance)
3m Formulastring As String, XAddress As String
3m result As Double
-ormulaString = expression.Formula
Wddress = variable.Address 'Default is absolute
'ormulaString = Application.ConvertFormula(FormulaString, xlAl, xlAl , -
xl Absolute)
Call GaussLeGendrel O(FormulaString, XAddress, from-lower, to-upper, -
tolerance, result)
Integrate = result
End Function
.............................................................
Sub GaussLeGendrel O(expression, XRef, from-lower, to-upper, tolerance,
result)
'Uses ten-point Gauss-Legendre quadrature formula.
Adapted from Shoup, p.203
Dim XJ As Variant, AJ As Variant
Dim TotalArea As Double, OldArea As Double, area As Double

Dim T As String, temp As String
Dim I As Integer, J As Integer, K As Integer, JJ As Integer
Dim N As Integer, NRepl As Integer
Dim A As Double, 6 As Double, C As Double, D As Double, F As Double
Dim H As Double
XJ = Array(-0.97390652851 71 72, -0.865063366688984, -0.679409568299024, -
0.433395394129247, -0.148874338981631,0.973906528517172,