A race: Jacobi verses GS verses SOR

To demonstrate the difference between the normal naive Jacobi and the SOR, we test the methods with a basic voltage configuration. Consider a grounded box with a rod half the length centered in the box. When we performed the relaxation, it took Jacobi's method 1623 iterations, GS 1074, and SOR only 199 iterations; this with a tolerance (maximum difference between previous values and new values) of 0.0001. Obviously one can see the advantage of the SOR method. Our results are presented below, and our program used ends this report.

Figure 4.1: Same results, different rates. Jacobi requires 1623 iterations, GS 1074, and SOR only 199 for a simple potential problem and a 100 by 100 grid.