Efficient Numerical Methods for Evolution Partial Differential Equations

Abstract

The convergence estimates obtained for the Korteweg-de Virus equation have been generalized, under the assumption that the solution u is sufficiently regular. For p 4, it is not known whether a global smooth solution exists corresponding to smooth initial data. It is in fact conjectured that for these cases, the solution may develop a singularity in finite time. A code that uses a spatially and temporally adaptive strategy has been implemented. We are currently investigating the stability of solitary type solutions. As conjectured, these solutions are highly unstable for initial amplitudes larger than one.

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Document Details

Document Type
Technical Report
Publication Date
Sep 30, 1989
Accession Number
ADA219790

Entities

People

  • Lhannes Karakashian

Organizations

  • University of Tennessee

Tags

DTIC Thesaurus Topics

  • Amplitude
  • Boundary Value Problems
  • Convergence
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Galerkin Method
  • Linear Systems
  • Mathematics
  • Measurement
  • Parallel Computing
  • Partial Differential Equations
  • Runge Kutta Method
  • Schrodinger Equation
  • Stratified Fluids

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Fluid Dynamics.
  • Linear Algebra