MATRIX DECOMPOSITION ALGORITHMS IN ORTHOGONAL SPLINE COLLOCATION FOR SEPARABLE ELLIPTIC BOUNDARY-VALUE-PROBLEMS

Fast direct methods are presented for the solution of linear systems a rising in high-order, tensor-product orthogonal spline collocation app lied to separable, second order, linear, elliptic partial differential equations on rectangles. The methods, which are based on a matrix dec omposition approach, involve the solution of a generalized eigenvalue problem corresponding to the orthogonal spline collocation discretizat ion of a two-point boundary value problem. The solution of the origina l linear system is reduced to solving a collection of independent almo st block diagonal linear systems which arise in orthogonal spline coll ocation applied to one-dimensional boundary value problems. The result s of numerical experiments are presented which compare an implementati on of the orthogonal spline collocation approach with a recently devel oped matrix decomposition code for solving finite element Galerkin equ ations.