NUMERICAL ANALYSIS OF STIFF EQUATIONS,

Abstract

The interaction between a stiff equation and several common integration procedures is examined. Runge-Kutta is the first procedure considered. A convergence condition is derived that can be used to control the integration step size. Truncation error estimates are also shown to be misleading and of limited usefulness for this procedure. A generalized Adams predictor-corrector procedure is examined in detail with regard to stability. A technique for maximizing the step size is introduced and applied to the generalized Adams procedure. The resulting procedure is appreciably faster than the more conventional one. The analysis also shows that the computation speed of any Adams method decreases as the order of the procedure increases. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 29, 1964
Accession Number
AD0431750

Entities

People

  • G. Emanuel

Organizations

  • The Aerospace Corporation

Tags

DTIC Thesaurus Topics

  • Computations
  • Convergence
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Truncation

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Regression Analysis.