Page 304 - Excel for Scientists and Engineers: Numerical Methods

CHAPTER 12 PARTIAL DIFFERENTIAL EQUATIONS 28 1

3ption Explicit
3ption Base 1
Function CrankNicholson(coeff, delta-x, delta-t, prev-values)
Solves a parabolic PDE by the Crank-Nicholson method.
Dim I As Integer, J As Integer, N As Integer
Dim F As Double
Dim CoeffMatrixO As Double, ConstantsVector() As Double

N = prev-values.Count
ReDim CoeffMatrix(N - 2, N - 2), ConstantsVector(N - 2, 1)
F = coeff * delta-t I delta-x A 2
'Create coefficients matrix. This is an N x N matrix.
For I = 1 To N - 2
ForJ=l TON-2
Select Case J
Case I
CoeffMatrix(1, J) = 2 + 2 F
Case I - 1
CoeffMatrix(1, J) = -F
Case I + 1
CoeffMatrix(1, J) = -F
Case Else
CoeffMatrix(1, J) = 0
End Select
Next J, I
'Create constants vector. This is a COLUMN vector.
ForJ=l TON-2
ConstantsVector(J, 1) = F * prev-values(J) + (2 - 2 * F) * prev-values(J + 1) + F * -
prev-values(J + 2)
Next J
ConstantsVector(1, 1) = ConstantsVector(1, 1) + F * prev-values(1)
ConstantsVector(N - 2, 1) = ConstantsVector(N - 2, IF+ F * prev-values(N)

'Return results as an array in a row, thus use Transpose.
CrankNicholson = Application.Transpose(App1ication. -
MMult(Application.MInverse(CoeMVlatrix),ConstantsVector))

End Function
Figure 12-12. VBA fbnction procedure to evaluate a PDE
by the Crank-Nicholson method.
(folder 'Chapter 12 (PDE) Examples, workbook 'Parabolic PDE', module 'Modulel')