New developments in the numerical solution of differential/algebraic systems
In this paper we survey some recent developments in the numerical solution of nonlinear differential/algebraic equation (DAE) systems of the form 0 = F(t,y,y'), where the initial values of y are known and par. deltaF/par. deltay' may be singular. These systems arise in the simulation of electrical networks, as well as in many other applications. DAE systems include standard form ODEs as a special case, but they also include problems which are in many ways quite different from ODEs. We examine the classification of DAE systems according to the degree of singularity of the system, and present some results on the analytical structure of these systems. We give convergence results for backward differentiation formulas applied to DAEs and examine some of the software issues involved in the numerical solution of DAEs. One-step methods are potentially advantageous for solving DAE systems with frequent discontinuities. However, recent results indicate that there is a reduction in the order of accuracy of many implicit Runge-Kutta methods even for simple DAE systems. We examine the current state of solving DAE systems by implicit Runge-Kutta methods. Finding a consistent set of initial conditions is often a problem for DAEs arising in applications. We explore some numerical methods for obtaining a consistent set of initial conditions. 21 refs.
- Research Organization:
- Lawrence Livermore National Lab., CA (USA)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 6449205
- Report Number(s):
- UCRL-100298; CONF-8704369-1; ON: DE89008022
- Resource Relation:
- Conference: AMS-SIAM-IMA summer seminar on computational aspects of VLSI design, Minneapolis, MN, USA, 1 Apr 1987; Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
DIFFERENTIAL EQUATIONS
NUMERICAL SOLUTION
CONVERGENCE
MATRIX ELEMENTS
NONLINEAR PROBLEMS
RUNGE-KUTTA METHOD
EQUATIONS
ITERATIVE METHODS
990230* - Mathematics & Mathematical Models- (1987-1989)
990220 - Computers
Computerized Models
& Computer Programs- (1987-1989)