A Crank-Nicolson Leapfrog Stabilization: Unconditional Stability and Two Applications

Abstract

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.

Department(s)

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)

0377-0427

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 Elsevier, All rights reserved.

Publication Date

01 Jun 2015

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