ADI Methods for Cubic Spline Collocation Discretizations of Elliptic PDE

This paper presents the formulation, the analysis and the 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 Diierential Equations (PDEs). The theoretical analysis is carried out for a board class of PDE problems. Numerical experiments connrm the theoretically determined characteristics of the ADI iterative schemes. The computational eeective-ness of the proposed schemes is shown through a detailed theoretical complexity analysis connrmed with our experimental data.