Variable Step-Size Selection Methods for Implicit Integration Schemes

Abstract

Implicit integration schemes are widely used in mathematics and engineering to solved ordinary differential equations. Every integration method requires one to choose a step-size for the independent variable which affects the efficiency and accuracy of the scheme. As every implicit integration scheme has a global error inherent to the scheme, we choose the total number of computations in order to achieve a prescribed global error as a measure of efficiency. A systematic method for choosing step-size is presented which is based on minimizing an efficiency function. The approach is applied to two popular numerical integration schemes.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 2005
Accession Number
ADA442333

Entities

People

  • David B. Doman
  • Ram V. Iyer
  • Raymond Holsapple

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Aircrafts
  • Applied Mathematics
  • Computations
  • Differential Equations
  • Efficiency
  • Engineering
  • Equations
  • Errors
  • Governments
  • Mathematics
  • Military Research
  • Numerical Analysis
  • Numerical Integration
  • Runge Kutta Method
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Civilian Systems Systems Program Capability Development and Upgrade Support Activity Expense and Pay Management.
  • Linear Algebra
  • Regression Analysis.