ADI Methods for Cubic Spline Collocation Discretizations of Elliptic PDE

This paper presents the formulation, analysis, and implementation of alternating direction implicit (ADI) methods for solving the linear system of algebraic equations that arise from the discretization of multidimensional linear elliptic partial differential equations (PDEs). The theoretical analysis is carried out for a broad class of PDE problems. Numerical experiments confirm the theoretically determined characteristics of the ADI iterative schemes. The computational effectiveness of the proposed schemes is shown through a detailed theoretical complexity analysis confirmed with our experimental data.

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