Journal Article10.1137/S1064827595289996
Consistent Initial Condition Calculation for Differential-Algebraic Systems
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TL;DR: A new algorithm for the calculation of consistent initial conditions for a class of systems of differential-algebraic equations which includes semi-explicit index-one systems is described, which requires a minimum of additional information from the user.
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Abstract: In this paper we describe a new algorithm for the calculation of consistent initial conditions for a class of systems of differential-algebraic equations which includes semi-explicit index-one systems. We consider initial condition problems of two types---one where the differential variables are specified, and one where the derivative vector is specified. The algorithm requires a minimum of additional information from the user. We outline the implementation in a general-purpose solver DASPK for differential-algebraic equations, and present some numerical experiments which illustrate its effectiveness.
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References
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more
TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
•Book
Numerical methods for unconstrained optimization and nonlinear equations
John E. Dennis,Robert B. Schnabel +1 more
- 01 Mar 1983
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
8.2K
•Book
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
John E. Dennis,Robert B. Schnabel +1 more
- 01 Feb 1996
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
6.8K
•Book
Numerical solution of initial-value problems in differential-algebraic equations
K. E. Brenan,Stephen L. Campbell,Linda R. Petzold +2 more
- 01 Jan 1987
TL;DR: In this article, the authors introduce the theory of DAE's and the index Linear constant coefficient, linear time varying, and nonlinear index systems, as well as a general linear multistep method.
3.3K
Inexact newton methods
TL;DR: A classical algorithm for solving the system of nonlinear equations is Newton's method as mentioned in this paper, which is known as Newton's algorithm for nonlinear systems of equations (see Fig. 1 ).