Jacobi point iteration method

There are two basic families of solution techniques for linear algebraic equations Direct- and iterative methods. A well known example of direct methods is Gaussian elimination. The simultaneous storage of all coefficients of the set of equations in core memory is required. Iterative methods are based on the repeated application of a relatively simple algorithm leading to eventual convergence after a number of repetitions (iterations). Well known examples are the Jacobi and Gauss-Seidel point-by-point iteration methods. 

In a space charge free region, the potential at point j,i is then simply the average of the four neighboring potentials. This iterative approach is known as Jacobi s method and dates back to the last century. 

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