Recent developments in the numerical solution of differential/algebraic systems

Conference · Fri Oct 09 00:00:00 EDT 1987

OSTI ID:5789902

Petzold, L R

In this paper we survey some recent development in the numerical solution of nonlinear differential/algebraic equation (DAE) systems of the form O = F/t,y,y'), where par. deltaF/par. deltay' may be singular. Initial value problems in DAEs arise in a wide variety of applications, including circuit and control theory, chemical kinetics, modeling of constrained mechanical systems, fluid dynamics and robotics. 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 explore some classes of initial value problems which can be solved by backward differentiation formulas, and discuss some results on the order of convergence of implicit Runge-Kutta methods applied to DAE systems. Finding a consistent set of initial conditions is often a problem for DAE systems arising in applications. We outline some recent work on a general algorithm for finding consistent initial conditions. Finally, we discuss some new developments in the numerical solution of DAE boundary value problems. 29 refs.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5789902
• Report Number(s): UCRL-97517; CONF-871230-1; ON: DE88001885
• Resource Relation: Conference: 8. international conference on computing methods in applied mechanics, Versailles, France, 14 Dec 1987; Other Information: Portions of this document are illegible in microfiche products
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
DIFFERENTIAL EQUATIONS
NUMERICAL SOLUTION
ALGORITHMS
BOUNDARY-VALUE PROBLEMS
NONLINEAR PROBLEMS
RUNGE-KUTTA METHOD
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
990230* - Mathematics & Mathematical Models- (1987-1989)