On Efficient Time-Stepping Methods for Nonlinear Second Order Hyperbolic Partial Differential Equations.

Abstract

Techniques useful for efficiently time-stepping Galerkin methods for various types of time-dependent partial differential equations are presented and analyzed. Second-order quasilinear hyperbolic problems with smooth solutions are studied as a simple model problem for illustrating the widely applicable techniques. The procedure involves the use of a preconditioned iterative method for approximately solving the different linear systems of equations arising at each time-step in a discrete-time Galerkin method. Optimal order L2 spatial errors and almost optimal order work estimates are obtained for the second-order hyperbolic equation. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1979
Accession Number
ADA079731

Entities

People

  • Richard E. Ewing

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Computational Complexity
  • Difference Equations
  • Differential Equations
  • Elastic Properties
  • Equations
  • Errors
  • Formulas (Mathematics)
  • Galerkin Method
  • Iterations
  • Linear Systems
  • Mathematics
  • Numerical Analysis
  • Partial Differential Equations
  • Smoothing (Mathematics)
  • Theorems
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

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