A Stepsize Control Strategy for Stiff Systems of Ordinary Differential Equations

Abstract

In solving stiff systems of ordinary differential equations using BDF methods, Jacobians needed for quasi-Newton iteration are frequently computed using finite differences. Round-off errors in the finite-difference approximation can lead to Newton failures forcing the code to choose its time steps based on stability rather than accuracy considerations. When standard stepsize control is used the code can experience thrashing which increases the total number of time steps, Jacobian evaluations, and function evaluations. In this paper we investigate this situation, explaining some surprising time step selection behavior produced by the standard control mechanism. A new control mechanism is proposed which attempts to find and use a stability stepsize. A comparison of the new strategy with the standard strategy and with two PI controllers introduced earlier is made using the stiff test set.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1994
Accession Number
ADA281551

Entities

People

  • Linda Petzold
  • Peter K. Moore

Organizations

  • University of New Orleans

Tags

Communities of Interest

  • Advanced Electronics
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computer Science
  • Control Systems
  • Convergence
  • Differential Equations
  • Equations
  • Errors
  • Iterations
  • Linear Systems
  • Mathematics
  • Partial Differential Equations
  • Runge Kutta Method
  • Standards
  • Test And Evaluation
  • Test Sets

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra