Projected collocation for higher-order higher-index differential- algebraic equations
type: Item
instance of: scholarly article
title: Projected collocation for higher-order higher-index differential- algebraic equations
zbMATH Open document ID: 0772.65049
DOI: 10.1016/0377-0427(92)90269-4
author: Uri M. Ascher
author: Linda Petzold
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-18T00:00:00Z
review text: The authors extend some of their previous results [SIAM J. Numer. Anal. 28, No. 4, 1097-1120 (1991; Zbl 0732.65067)] to differential-algebraic equations of the type \(x^{(m)} = f(x^{(m-1)},\dots,\) \(x',x,y,t)\), \(0 = g(x,t)\), where \(x(t) \in \mathbb{R}^ n\), together with a set of boundary conditions. Main attention is paid to the linear case \(f(z_ m,\dots,z_ 1,y,t) = \sum^ m_{j=1}A_ j(t)z_ j + B(t)y + q(t)\), \(g(x,t) = C(t)x + r(t)\). A projection collocation scheme is discussed which yields a stable superconvergent integration method. Numerical examples are considered comparing the Gauss and Radau collocation schemes.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 85933
zbMATH Keywords: higher-order
zbMATH Keywords: higher-index
zbMATH Keywords: differential-algebraic equations
zbMATH Keywords: projection collocation scheme
zbMATH Keywords: Numerical examples
reviewed by: Mihail M. Konstantinov
describes a project that uses: COLSYS
MaRDI profile type: Publication
full work available at URL: 0377-0427(92)90269-4
OpenAlex ID: W2063789180
cites work: Collocation for Two-Point Boundary Value Problems Revisited
cites work: On Numerical Differential Algebraic Problems with Application to Semiconductor Device Simulation
cites work: Collocation Software for Boundary-Value ODEs
cites work: Q3994561
cites work: Projected Implicit Runge–Kutta Methods for Differential-Algebraic Equations
cites work: Stabilization of constraints and integrals of motion in dynamical systems
cites work: Q3993493
cites work: Collocation at Gaussian Points
cites work: Numerical solution of differential-algebraic equations for constrained mechanical motion
cites work: Maintaining Solution Invariants in the Numerical Solution of ODE<scp>s</scp>
cites work: Differential-Algebraic Equation Index Transformations
cites work: Automatic integration of Euler-Lagrange equations with constraints
cites work: Basic properties of some differential-algebraic equations
cites work: Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
cites work: On projected Runge-Kutta methods for differential-algebraic equations
description: scientific article; zbMATH DE number 85933