Numerical Math - The Jacobi method

A simple explanation giving by Landau et al [1] defines the Jacobi method as an initial sweep of a values without updating if available. The Jacobi method is very basic. For example, from the square wire problem in Landau et al the numerical algorithm to be solved is

\[ U_{i, j} = \dfrac{1}{4} \left( U_{i + 1, j} + U_{i - 1, j} + U_{i, j + 1} + U_{i, j - 1} \right) \]

The initialization and BCs symmetry are preserved in this way.

---

References:

[1] R. H. Landau, M. J. Páez, and C. C. Bordeianu. A Survey of Computational Physics - Introductory Computational Science, Princeton University Press, Princeton, New Jersey. 2008