Focusing: A mechanism for instability of nonlinear finite difference equations

William L. Briggs; Alan C. Newell; Talib Sarie

doi:10.1016/0021-9991(83)90082-7

Focusing: A mechanism for instability of nonlinear finite difference equations

William L. Briggs
, Alan C. Newell
, Talib Sarie

Mathematics

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

41 Scopus citations

Abstract

A mechanism for the destabilization of numerical algorithms for partial differential equations is suggested. The novelty of the work is that it attempts to explain the dynamical process by which noise can localize on a spatial grid and cause finite amplitude instability thresholds to be exceeded at distinct locations.

Original language	English (US)
Pages (from-to)	83-106
Number of pages	24
Journal	Journal of Computational Physics
Volume	51
Issue number	1
DOIs	https://doi.org/10.1016/0021-9991(83)90082-7
State	Published - Jul 1983

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/0021-9991(83)90082-7

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title = "Focusing: A mechanism for instability of nonlinear finite difference equations",

abstract = "A mechanism for the destabilization of numerical algorithms for partial differential equations is suggested. The novelty of the work is that it attempts to explain the dynamical process by which noise can localize on a spatial grid and cause finite amplitude instability thresholds to be exceeded at distinct locations.",

author = "Briggs, \{William L.\} and Newell, \{Alan C.\} and Talib Sarie",

note = "Funding Information: This research was supported in part by National Science Foundation Grants PHY77-27084 and MCS-07548 AOI. One of us (A.C.N) is very appreciative of the hospitality and scientific atmosphere he enjoyed while visiting the Institute for Theoretical Physics at the University of California. Santa Barbara. The work was also supported in part by U.S. Army Contract DAAG29-82-C-0068 and ONR Contract N00014-76-C-0867. The authors are also particularly grateful to David Rand whose healthy scepticism and insightful comments encouraged us to examine Fig. I in greater detail.",

year = "1983",

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doi = "10.1016/0021-9991(83)90082-7",

language = "English (US)",

volume = "51",

pages = "83--106",

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T2 - A mechanism for instability of nonlinear finite difference equations

AU - Briggs, William L.

AU - Newell, Alan C.

AU - Sarie, Talib

N1 - Funding Information: This research was supported in part by National Science Foundation Grants PHY77-27084 and MCS-07548 AOI. One of us (A.C.N) is very appreciative of the hospitality and scientific atmosphere he enjoyed while visiting the Institute for Theoretical Physics at the University of California. Santa Barbara. The work was also supported in part by U.S. Army Contract DAAG29-82-C-0068 and ONR Contract N00014-76-C-0867. The authors are also particularly grateful to David Rand whose healthy scepticism and insightful comments encouraged us to examine Fig. I in greater detail.

PY - 1983/7

Y1 - 1983/7

N2 - A mechanism for the destabilization of numerical algorithms for partial differential equations is suggested. The novelty of the work is that it attempts to explain the dynamical process by which noise can localize on a spatial grid and cause finite amplitude instability thresholds to be exceeded at distinct locations.

AB - A mechanism for the destabilization of numerical algorithms for partial differential equations is suggested. The novelty of the work is that it attempts to explain the dynamical process by which noise can localize on a spatial grid and cause finite amplitude instability thresholds to be exceeded at distinct locations.

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DO - 10.1016/0021-9991(83)90082-7

M3 - Article

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SP - 83

EP - 106

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

Focusing: A mechanism for instability of nonlinear finite difference equations

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