This example, using the same data, illustrates the use of a smaller grid size. The spreadsheet ('Crank-Nicholson 3'), not shown here, can be examined on the accompanying CD-ROM. The x-increment is 2 cm, thus creating a table of values that is 11 columns wide, including the boundary values, and requiring a 9 x 9 matrix of coefficients.
The spreadsheet employs a single formula for all cells of the coefficients table:
The formula uses the following named formulas CoeffTableCol =COLUMN()-MIN(COLUMN(coefficients)) CoeffTableRow =ROW()-MIN(ROW(coefficients))
Thus a Crank-Nicholson calculation can be set up on a spreadsheet using a single formula to create the coefficients table, a (different) single formula to create the constants table, and a single formula for the values table.
The results using the smaller grid size are shown in the following chart.
0 200 400 600 800 1000 1200 Time, seconds
Figure 12-11. Chart of the results produced by the spreadsheet shown in Figure 12-10. (folder 'Chapter 12 (PDE) Examples, workbook 'Parabolic PDE', sheet 'Crank-Nicholson 3')
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