The Successive Peripheral Block Over-relaxation Method

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Abstract
In the finite difference representation of a partial differential equation, the mesh points on a two dimensional grid are ordered in a new manner, viz. around successive peripherals of the region of integration. The resulting coefficient matrix is such that the theory of successive block over-relaxation is valid and this technique is used to solve Dirichlet problems in regions particularly suited to the new ordering viz. the unit square with a square hole removed from the centre and a circular annular region. Comparisons are made between this new ordering and standard methods and improved rates of convergence are obtained.

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