A Crank-Nicolson Leapfrog Stabilization: Unconditional Stability and Two Applications
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.
N. Jiang et al., "A Crank-Nicolson Leapfrog Stabilization: Unconditional Stability and Two Applications," Journal of Computational and Applied Mathematics, vol. 281, pp. 263-276, Elsevier, Jun 2015.
The definitive version is available at https://doi.org/10.1016/j.cam.2014.09.026
Mathematics and Statistics
Keywords and Phrases
Asymptotic stability; Groundwater; Linear systems; Stability; Surface waters; CFL condition; CNLF; Coriolis terms; Groundwater-surface waters; Increasing solutions; Stability and control; Unconditional stability; Unstable modes; Stabilization
International Standard Serial Number (ISSN)
Article - Journal
© 2015 Elsevier, All rights reserved.
01 Jun 2015