The numerical solution of some higher-index time-varying semistate systems by difference methods
type: Item
instance of: scholarly article
title: The numerical solution of some higher-index time-varying semistate systems by difference methods
zbMATH Open document ID: 0626.65060
DOI: 10.1007/BF01599006
author: K. Clark
published in: Circuits, Systems, and Signal Processing
publication date: 1987-01-01T00:00:00Z
review text: Backwards differentiation formulas (BDF) are one of the more popular methods used on singular systems of differential equations (also known as singular or descriptor systems). It known that even in the linear time varying case that BDF approximations need not converge. This paper examines the behavior of BDF on linear time varying semi-state systems of the form \(A(t)x'(t)+B(t)x(t)=f(t).\) Necessary and sufficient conditions are given for the solvability of fully implicit index one and semi- explicit index two linear systems in this form. Using this solvability criteria, the convergence and stability of BDF for solvable semi-explicit index two systems is established. These methods exhibit a boundary layer of instability of length 2k (where k is the order of the method) in the algebraic variables. Finally, it is shown that these systems belong to a class of BDF solvable systems which strictly contains the systems safely transformable to standard canonical form.
reviewed by: Stephen L. Campbell
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 4018259
zbMATH Keywords: finite difference methods
zbMATH Keywords: Backwards differentiation formulas
zbMATH Keywords: singular systems
zbMATH Keywords: descriptor systems
zbMATH Keywords: linear time varying semi-state systems
zbMATH Keywords: fully implicit index one and semi-explicit index two linear systems
zbMATH Keywords: convergence
zbMATH Keywords: stability
zbMATH Keywords: boundary layer of instability
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4018259