Abstract
This chapter discusses the ad-hoc successive over relaxation (SOR) method. In solving a system of five-point difference equations by the SOR method, an estimate of the optimal relaxation parameter is needed. This parameter is determined from the eigenvalues of the Jacobi matrix. However, the eigenvalues of the Jacobi matrix are not easily estimated in general, although methods have been developed to approximate the relaxation factor dynamically. The ad-hoc SOR method attempts to circumvent the need to estimate a relaxation factor by computing, for each equation, its own relaxation factor based on the difference equation coefficients of that equation and the boundary conditions and region shape.
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