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9.6. Using Classical Methods for Solving Equations

Problem

You've seen how to leverage Excel's built-in features to solve linear and nonlinear equations and systems, but you'd still like to know how to go about implementing some classical equation-solving algorithms in Excel.

Solution

You can use VBA to program any algorithm, just as you might in other programming languages. In the discussion to follow, I'll show you how to implement two classical methods in VBA: Newton's method and the secant method.

Discussion

The examples in this recipe will show how you might implement Newton's method and the secant method. These are well-known methods and are treated in most advanced mathematics and numerical methods texts. Further, you can find implementations of these methods in various languages, such as Fortran and C, on the Web. It's not a great leap to implement these methods in VBA in the form of a custom function, which you can then call from an Excel spreadsheet.

For the examples in this recipe, let's reconsider the cubic polynomial equation already discussed in Recipe 9.1. The equation is repeated here for convenience:

A quick plot of this equation, as shown earlier in Figure 9-6, shows about where these three roots lie. You could easily use Solver to accurately find each of these roots. Or, you could use Newton's method or the secant method (or any of a number of other methods you could ...

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