Page 282 - Excel for Scientists and Engineers: Numerical Methods

CHAPTER 11 ORDINARY DIFFERENTIAL EQUATIONS. PART I1 259

In order to simplify the construction of the coefficients matrix, you can use
the spreadsheet layout shown in Figure 11-14. The formula in cell 17, which has
been assigned the name top, is
=IF(ROW()-ROW(tOp)=COLUMN()-COLUMN(tOp),lNDlRECT("F"&ROW()),
1
IF(ABS((ROW()-ROW(tOp))-(COLUMN()-COLUMN(tO~)))~l, ,O))

Figure 11-14. Coefficients matrix to solve the second-order differential equation
y" -y = 0.
(folder 'Chapter 11 Examples', workbook 'ODE-BVP, worksheet 'Finite Difference 2')

To create the spreadsheet, do the following:
Enter the desired range of x values in column A. This is best done by
inserting rows within the range of x values, so as to preserve the formulas in
the last row.
Enter the boundary values of y in the first and last rows.
Enter values or expressions for the coefficients a, b and c in cells C13, D13
and E13, and Fill Down.
Select cell 17 and Fill Down, then Fill Right, to create the coefficients
matrix.
Select the cell containing the formula for the results vector and Fill Down.
Enter the formula by pressing CONTROL+SHIFT+ENTER.

The results vector is shown in Figure 1 1 - 15 and a plot of the results in Figure
11-16.