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

ANDREW D. JORGENSON

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

Published online: 2014-05

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  • 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.
  • Keywords

convection-diffusion equations unconditional stability IMEX methods Crank-Nicolson Adams-Bashforth 2

  • AMS Subject Headings

76D05 65L20 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-5-171, author = {ANDREW D. JORGENSON}, title = {Unconditional Stability of a Crank-Nicolson Adams-Bashforth 2 Numerical Method.}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2014}, volume = {5}, number = {3}, pages = {171--187}, 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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/229.html} }
TY - JOUR T1 - Unconditional Stability of a Crank-Nicolson Adams-Bashforth 2 Numerical Method. AU - ANDREW D. JORGENSON JO - International Journal of Numerical Analysis Modeling Series B VL - 3 SP - 171 EP - 187 PY - 2014 DA - 2014/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/229.html KW - convection-diffusion equations KW - unconditional stability KW - IMEX methods KW - Crank-Nicolson KW - Adams-Bashforth 2 AB - 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.
ANDREW D. JORGENSON. (2014). Unconditional Stability of a Crank-Nicolson Adams-Bashforth 2 Numerical Method.. International Journal of Numerical Analysis Modeling Series B. 5 (3). 171-187. doi:
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