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The problem studied in this paper is the numerical solution of the two-group diffusion equations describing the reactivity and power distribution of a nuclear power reactor. The problem is treated in two dimensions (Cartesian coordinates). The method of solution by replacement of the differential equations by finite difference equations is outlined. The properties of the resulting matrices are studied in detail. The method of successive overrelaxation is described and the theory developed. The convergence properties of the method and its application is indicated.