Solution of Partial Differential Equations by Arbitrary Grid Finite Difference Technique.

Abstract

The models arising in structural analysis involve systems of fourth order partial differential equations (PDE's) which collectively are equivalent to an eighth order PDE. Finite difference techniques have been used for numerical analysis of the PDE's for a number of years, but have been hampered by fairly heavy restrictions on the types of discretization grids that could be used. Relaxation of these restrictions in the application of the equilibrium (direct) finite difference method is presented with results from application to the biharmonic plate problem under a variety of boundary conditions. Two methods for generating suitable grids are presented with sample results. Methods for iteratively redistributing the nodes of a grid based on a-posteriori error estimation in order to reduce that error are also presented. One-dimensional results for this process are given both for direct discretization and variational finite difference analysis. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 26, 1972
Accession Number
AD0746045

Entities

People

  • Paul S. Jensen

Organizations

  • Lockheed Martin Missiles and Space

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Complex Variables
  • Difference Equations
  • Differential Equations
  • Equations
  • Finite Difference Theory
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Numerical Methods And Procedures
  • Partial Differential Equations
  • Structural Analysis
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)