Finite Difference Schemes for Long-Time Integration

Abstract

Finite difference schemes for the evaluation of first and second derivatives are presented. These second order compact schemes were designed for long-time integration of evolution equations by solving a quadratic constrained minimization problem. The quadratic cost function measures the global truncation error while taking into account the initial data. The resulting schemes are applicable for integration times fourfold, or more, longer than similar previously studied schemes. A similar approach was used to obtain improved integration schemes. Finite differences, Long-time integration, Compact schemes.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1993
Accession Number
ADA269779

Entities

People

  • Shlomo Ta'asan
  • Zigo Haras

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Differential Equations
  • Engineering
  • Equations
  • Fluid Flow
  • Fourier Analysis
  • Mathematics
  • Numerical Analysis
  • Partial Differential Equations
  • Simulations
  • Test And Evaluation
  • Truncation
  • Two Dimensional
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design