Using Diagonally Implicit Multistage Integration Methods for Solving Ordinary Differential Equations. Part 1: Introduction and Explicit Methods.

Abstract

A survey of theoretical results for the recently invented and highly promising class of diagonally implicit multistage integration methods (DIMSIMs) is provided. New results are obtained that provide improved implementation and simplified analysis. Particular attention is given to issues affecting use on parallel computers in waveform relaxation. The process of implementation parameter derivation and testing for the second and fifth order members of the DIMEX family of ordinary differential equation solver computer codes using explicit DIMSIMs is described. Extensive test results using the standard suite DETEST are reported that show considerable promise. A listing of the FORTRAN 77 research code DIMEX5 is provided.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1997
Accession Number
ADA324085

Entities

People

  • Jack Vanwieren

Organizations

  • Naval Air Warfare Center Weapons Division

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes
  • Weapons Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Aerial Warfare
  • Algorithms
  • Chemical Reactions
  • Computational Complexity
  • Computers
  • Differential Equations
  • Eigenvalues
  • Equations
  • Estimators
  • Extrapolation
  • Linear Systems
  • Runge Kutta Method
  • Safety Factor
  • Simultaneous Equations
  • Standards
  • Waveforms

Readers

  • Computational Modeling and Simulation
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)