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A Crank–Nicolson Leapfrog stabilization: unconditional stability and two applications

  • Nan Jiang [1] ; William Layton [1] ; Marina Moraiti [1] ; Michaela Kubacki [2] ; Hoang Tran [3]
    1. [1] University of Pittsburgh

      University of Pittsburgh

      City of Pittsburgh, Estados Unidos

    2. [2] Middlebury College

      Middlebury College

      Town of Middlebury, Estados Unidos

    3. [3] Oak Ridge National Laboratory

      Oak Ridge National Laboratory

      Estados Unidos

  • Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 281, Nº 1 (June 2015), 2015, págs. 263-276
  • Idioma: inglés
  • DOI: 10.1016/j.cam.2014.09.026
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  • Resumen
    • We propose and analyze a linear stabilization of the Crank–Nicolson Leapfrog (CNLF) method that removes all time step/CFL conditions for stability and controls the unstable mode. It also increases the SPD part of the linear system to be solved at each time step while increasing solution accuracy. We give a proof of unconditional stability of the method as well as a proof of unconditional, asymptotic stability of both the stable and unstable modes. We illustrate two applications of the method: uncoupling groundwater–surface water flows and Stokes flow plus a Coriolis term.


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