Volume 5, Issue 3
Unconditional Stability of a Crank-Nicolson Adams-Bashforth 2 Numerical Method.

Zichen Deng

Int. J. Numer. Anal. Mod. B,5 (2014), pp. 171-187

Preview Full PDF BiBTex 63 401
  • Abstract

Nonlinear partial differential equations modeling turbulentv fluid flow and similar processes present special challanges in numerical analysis. Regions of stability of implicit-explicit methods are reviewed, and an energy norm based on Dahlquist's concept of G-stability is developed. Using this norm, a time-stepping Crank-Nicolson Adams-Bashforth 2 implicit-explicit method for solving spatially-discretized convection-diffusion equations of this type is analyzed and shown to be unconditionally stable.

  • History

Published online: 2014-05

  • AMS Subject Headings

76D05, 65L20, 65M12

  • Cited by