Stability of the IMEX Methods, CNLF and BDF2-AB2, for Uncoupling Systems of Evolution Equations

Abstract

Stability is proven for two second order, two step methods for uncoupling a system of two evolution equations with exactly skew symmetric coupling: the Crank-Nicolson Leap Frog (CNLF) combination and the BDF2-AB2 combination. The form of the coupling studied arises in spatial discretizations of the Stokes-Darcy problem. For CNLF we prove stability for the coupled system under the time step condition suggested by linear stability theory for the Leap-Frog scheme. This seems to be a first proof of a widely believed result. For BDF2-AB2 we prove stability under a condition that is better than the one suggested by linear stability theory for the individual methods. This report is an expended version of the one submitted for publication.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2011
Accession Number
ADA538555

Entities

People

  • C. Trenchea
  • W. Layton

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Couplings
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Flow
  • Fluid Dynamics
  • Fluid Flow
  • Identities
  • Mathematics
  • Navier Stokes Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Personal Information Managers
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.