Stable Parallel Algorithms for Two-Point Boundary Value Problems

Abstract

Some of the most widely used algorithms for two-point boundary value ordinary differential equations, namely, finite-difference and collocation methods and standard multiple shooting, proceed by setting up and solving a structured system of linear equations. It is well known that the linear system can be set up efficiently in parallel; we show here that a structured orthogonal factorization technique can be used to solve this system, and hence the overall problem, in an efficient, parallel, and stable way.