Almost Block Diagonal Linear Systems: Sequential and Parallel Solution Techniques, and Applications

Almost block diagonal (ABD) linear systems arise in a variety of contexts, specifically in numerical methods for two-point boundary value problems for ordinary differential equations and in related partial differential equation problems. The stable, efficient sequential solution of ABDs has received much attention over the last fifteen years and the parallel solution more recently. We survey the fields of application with emphasis on how ABDs and bordered ABDs (BABDs) arise. We outline most known direct solution techniques, both sequential and parallel, and discuss the comparative efficiency of the parallel methods. Finally, we examine parallel iterative methods for solving BABD systems. Copyright (C) 2000 John Wiley & Sons, Ltd

Hermite bicubic spline collocation method for Poisson's equations

In this paper is presented a bicubic spline collocation method for the numerical approximation of the solution of Dirichlet problem for the Poisson's equation. The approximating solution is effectively determined in a bicubic Hermite spline functions space by using a suitable basis constructed as a tensorial product of univariate spline spaces