THE NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS.

Abstract

The paper draws attention to several particularly promising areas of research in the numerical integration of ordinary differential equations. One area is the development of special methods for special problems such as stiff equations. A second concerns a rigorous theory for the computing procedures used in practice, taking account of the fact that the step-size is not infinitesimal, and including the use of error criteria for controlling step-size. A third concerns the determination of bounds on the propagated error, using interval arithmetic or ellipsoidal bounds, and the analogy with control theory. Another involves assessing relative merits of methods in terms of their costs with respect to specified problems. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 25, 1968
Accession Number
AD0667878

Entities

People

  • T. E. Hull

Organizations

  • University of Toronto

Tags

DTIC Thesaurus Topics

  • Arithmetic
  • Control Theory
  • Differential Equations
  • Equations
  • Intervals
  • Mathematics
  • Numerical Integration

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Defense Technology Research and Development.
  • Structural Dynamics.