ADI METHODS FOR CUBIC SPLINE COLLOCATION DISCRETIZATIONS OF ELLIPTIC PDES

This paper presents the formulation, analysis, and implementation of a lternating direction implicit (ADI) methods for solving the linear sys tem of algebraic equations that arise from the discretization of multi dimensional 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 character istics of the ADI iterative schemes. The computational effectiveness o f the proposed schemes is shown through a detailed theoretical complex ity analysis confirmed with our experimental data.