Numerical solution of nonlinear differential equations with algebraic contraints II: practical implications

@article{Petzold1986NumericalSO,
  title={Numerical solution of nonlinear differential equations with algebraic contraints II: practical implications},
  author={Linda R. Petzold and Per L{\"o}tstedt},
  journal={Siam Journal on Scientific and Statistical Computing},
  year={1986},
  volume={7},
  pages={720-733}
}
In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints. Systems of this form arise frequently in the modelling of problems from physics and engineering; we study some particular examples from fluid dynamics and constrained mechanical systems. We investigate some of the practical difficulties of implementing variable-stepsize backward differentiation formulas for the solution of these equations… 

Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas

In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints. Systems of this form arise frequently in

NUMERICAL METHODS SOLVING THE SEMI-EXPLICIT DIFFERENTIAL-ALGEBRAIC EQUATIONS BY IMPLICIT MULTISTEP FIXED STEPSIZE METHODS

We consider three classes of numerical methods for solving the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and

Non-stiff integrators for differential–algebraic systems of index 2

Non-stiff differential-algebraic equations (DAEs) can be solved efficiently by partitioned methods that combine well-known non-stiff integrators from ODE theory with an implicit method to handle the

NORTH-HOLLAND RECENT 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 aFlay’ may be singular.

Methods and Software for Differential-Algebraic Systems

The current state of the development and analysis of numerical methods such as multistep and implicit Eunge-Kutta applied to classes of DAE’s occuring in applications is reviewed.

On numerical differential algebraic problems with application to semiconductor device simulation

This paper considers questions regarding conditioning of, and numerical methods, for certain differential algebraic equations subject to initial and boundary conditions. The approach taken is that of

Numerical Methods for ODEs

...

References

SHOWING 1-10 OF 18 REFERENCES

Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas

In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints. Systems of this form arise frequently in

Simultaneous Numerical Solution of Differential-Algebraic Equations

A unified method for handling the mixed differential and algebraic equations of the type that commonly occur in the transient analysis of large networks or in continuous system simulation is

ODE METHODS FOR THE SOLUTION OF DIFFERENTIAL/ALGEBRAIC SYSTEMS

A reduction technique is described which allows systems to be reduced to ones that can be solved and provides a tool for the analytical study of the structure of systems.

Difference approximations for higher index differential-algebraic systems with applications in trajectory control

  • K. Brenan
  • Mathematics
    The 23rd IEEE Conference on Decision and Control
  • 1984
The equations which describe a trajectory prescribed path control (TPPC) problem naturally form a system of nonlinear semi-explicit, differential-algebraic equations (DAES) with index greater than

A description of dassl: a differential/algebraic system solver

The algorithms and strategies used in DASSL, for the numerical solution of implicit systems of differential/algebraic equations, are outlined, and some of the features of the code are explained.

Solution of the time-dependent incompressible Navier-Stokes equations via a penalty Galerkin finite element method

The existence of an initial non-physical transient when using the penalty method in modeling the time-dependence incompressible Navier-Stokes equations is investigated theoretically and demonstrated

Differential equations are not ODEs

  • Journal
  • 1982

Foundations of modern analysis