Behavior of the nonunique terms in general DAE integrators
type: Item
instance of: scholarly article
title: Behavior of the nonunique terms in general DAE integrators
zbMATH Open document ID: 0931.65089
DOI: 10.1016/S0168-9274(98)00044-0
author: Stephen L. Campbell
author: K. Yeomans
published in: Applied Numerical Mathematics
publication date: 1999-06-29T00:00:00Z
review text: The article is concerned with systems of differential-algebraic equations (DAEs), and their numerical solution. In general, numerical DAE solvers require to solve a system of nonlinear equations in each time step, the dimension of which depends on the index of the DAE and is larger than the dimension of the original DAE system. A part of the solution of the nonlinear system is usually not uniquely determined. It is shown that this part solves an auxiliary DAE which also depends on the predictor used in the Gauss-Newton iteration solving the system. As a consequence, criteria for the design of low-order integrators are established; in particular, explicit integration and implicit coordinate partitioning schemes of order lower than the index of the DAE, are justified.
Mathematics Subject Classification ID: 65L80
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 1311262
zbMATH Keywords: systems of differential-algebraic equations
zbMATH Keywords: index
zbMATH Keywords: Gauss-Newton iteration
zbMATH Keywords: low-order integrators
reviewed by: Michael Plum
describes a project that uses: GELDA
MaRDI profile type: Publication
cites work: Comparing stability properties of three methods in DAEs or ODEs with invariants
cites work: Constrained least squares methods for linear timevarying DAE systems
cites work: Analytical and numerical solutions to higher index linear variable coefficient DAE systems
cites work: Q4868578
cites work: Least squares completions for nonlinear differential algebraic equations
cites work: The index of general nonlinear DAEs
cites work: Solvability of General Differential Algebraic Equations
cites work: Progress on a general numerical method for nonlinear higher index DAEs. II
cites work: Constraint preserving integrators for general nonlinear higher index DAEs
cites work: Utilization of automatic differentiation in control algorithms
cites work: Jacobian reuse in explicit integrators for higher index DAEs
cites work: ODE Methods for the Solution of Differential/Algebraic Systems
cites work: A New Class of Discretization Methods for the Solution of Linear Differential-Algebraic Equations with Variable Coefficients
cites work: Regular solutions of nonlinear differential-algebraic equations and their numerical determination
cites work: A New Software Package for Linear Differential-Algebraic Equations
cites work: Continuous Newton-Raphson method for solving and underdetermined system of nonlinear equations
cites work: Global analysis of continuous analogues of the Levenberg-Marquardt and Newton-Raphson methods for solving nonlinear equations
full work available at URL: s0168-9274(98)00044-0
OpenAlex ID: W1978261320
description: scientific article; zbMATH DE number 1311262