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236 EXCEL NUMERICAL METHODS
Figure 10-13. Decreasing error in the Euler method
by a simple predictor-corrector method.
(folder 'Chapter 10 Examples', workbook 'ODE Examples', worksheet 'Predictor-Corrector Method')
The predictor formula was entered in column B. The first two values, shown
in bold, are the starting values; the predictor formula, in cell B6, corresponds
exactly to equation 10-28 and is
=B4+2*DX*-k*B5
The corrector formula, in cell C6, corresponds exactly to equation 10-29 and
is
=$ B5+ DX*( -k*$ B5-k*B6)/2
The preceding formula is used iteratively. The formula (note the use of
relative and mixed references) was Filled Right to perform the iterations. The
formulas in row 5 were added to display the difference between a corrected value
and the preceding one (for example, the formula in cell C5 is
=B1 I-C11
and shows how the corrector formula converges).
A Simple Predictor-Corrector Method
Utilizing an Intentional Circular Reference
An intentional circular reference can be used in the corrector formula to
eliminate the need to Fill Right the corrector formula in order to perform the
