Optimum Extrapolated Alternating Direction Implicit Schemes in the Presence of Singular Matrices

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Abstract
This paper shows how Extrapolated Alternating Direction Implicit (E.A.D.I.) methods can be used for the numerical solution of Laplace's equation under Neumann boundary conditions. E.A.D.I. methods are applied with the Douglas set of parameters and optimum E.A.D.I. schemes are given.