A Crank-Nicolson Leapfrog stabilization: Unconditional stability and two applications

Nan Jiang; Michaela Kubacki; William Layton; Marina Moraiti; Hoang Tran

doi:10.1016/j.cam.2014.09.026

A Crank-Nicolson Leapfrog stabilization: Unconditional stability and two applications

Nan Jiang, Michaela Kubacki, William Layton, Marina Moraiti, Hoang Tran

Data Analysis and Machine Learning

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

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.

Original language	English
Pages (from-to)	263-276
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	281
DOIs	https://doi.org/10.1016/j.cam.2014.09.026
State	Published - Jun 2015

Funding

This report is in final form. The research of the authors was partially supported by National Science Foundation grant DMS 1216465 and Air Force Office of Scientific Research grant FA 9550-12-1-0191 .

Keywords

CFL condition
CNLF
Stabilization

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10.1016/j.cam.2014.09.026

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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.",

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T1 - A Crank-Nicolson Leapfrog stabilization

T2 - Unconditional stability and two applications

AU - Jiang, Nan

AU - Kubacki, Michaela

AU - Layton, William

AU - Moraiti, Marina

AU - Tran, Hoang

PY - 2015/6

Y1 - 2015/6

N2 - 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.

AB - 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.

KW - CFL condition

KW - CNLF

KW - Stabilization

UR - http://www.scopus.com/inward/record.url?scp=84922371057&partnerID=8YFLogxK

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DO - 10.1016/j.cam.2014.09.026

M3 - Article

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SN - 0377-0427

VL - 281

SP - 263

EP - 276

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

A Crank-Nicolson Leapfrog stabilization: Unconditional stability and two applications

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Keywords

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