You've set up a finite difference solution to an elliptic boundary value problem, but instead of directly solving a system of algebraic equations, you want to use an iterative approach.

Set up your finite difference equations in Excel and use Solver to iteratively find a solution.

In Recipe 12.1, I explained how you can use Excel's matrix functions to directly solve systems of finite difference equations. For small systems, direct matrix operations are viable; however, for large systems the use of matrix functions in Excel is cumbersome. Other standard direct methods include *Gauss elimination* and *Fourier's method*, among others. These methods could be programmed in Excel; however, there's another class of methods known as *iterative methods*
that are more attractive.

Iterative solutions to finite differences equations abound. Various standard methods such as *Jacobi's method*
, *Gauss-Seidel iteration*
(also called *Liebmann's method*
), and the *alternating direction implicit* (ADI) *method* are commonly used in lieu of direct methods. Iterative methods have an advantage over direct methods in that they typically require less memory and are relatively easy to program. Moreover, when using Excel to help solve your problem, you already have access to a powerful iterative tool, Solver. This means that you can use Solver to find a solution to your finite difference equations without any programming ...

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