Computing in the past with forward integration

C. W. Gear; Ioannis G. Kevrekidis

doi:10.1016/j.physleta.2003.12.041

Computing in the past with forward integration

C. W. Gear, Ioannis G. Kevrekidis

Chemical & Biological Engineering

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

26 Scopus citations

Abstract

Using existing, forward-in-time integration schemes, we demonstrate that under certain conditions it is possible to compute the solution at earlier times, even in the presence of stiffness (for which reverse integration is unstable). This technique can be used when a reverse integrator is not available - for example, when all one has is a forward-in-time legacy code. It can also be used for the "reverse coarse" integration of the macroscopic closure of a system defined by a microscopic model which itself is naturally forward in time (e.g., a particle model of a gas). The method proposed has stability properties that enable it to converge to stationary points of unstable stiff systems.

Original language	English (US)
Pages (from-to)	335-343
Number of pages	9
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	321
Issue number	5-6
DOIs	https://doi.org/10.1016/j.physleta.2003.12.041
State	Published - Feb 16 2004

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Keywords

Differential equations
Reverse integration
Stationary points

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10.1016/j.physleta.2003.12.041

Cite this

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title = "Computing in the past with forward integration",

abstract = "Using existing, forward-in-time integration schemes, we demonstrate that under certain conditions it is possible to compute the solution at earlier times, even in the presence of stiffness (for which reverse integration is unstable). This technique can be used when a reverse integrator is not available - for example, when all one has is a forward-in-time legacy code. It can also be used for the {"}reverse coarse{"} integration of the macroscopic closure of a system defined by a microscopic model which itself is naturally forward in time (e.g., a particle model of a gas). The method proposed has stability properties that enable it to converge to stationary points of unstable stiff systems.",

keywords = "Differential equations, Reverse integration, Stationary points",

author = "Gear, {C. W.} and Kevrekidis, {Ioannis G.}",

note = "Funding Information: This work was partially supported by AFOSR (Dynamics and Control, Dr. B. King) and an NSF ITR grant. Discussions with Profs. P.G. Kevrekidis (UMass), Ju Li (OSU) and Dr. G. Hummer (NIH) are gratefully acknowledged.",

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AU - Gear, C. W.

AU - Kevrekidis, Ioannis G.

N1 - Funding Information: This work was partially supported by AFOSR (Dynamics and Control, Dr. B. King) and an NSF ITR grant. Discussions with Profs. P.G. Kevrekidis (UMass), Ju Li (OSU) and Dr. G. Hummer (NIH) are gratefully acknowledged.

PY - 2004/2/16

Y1 - 2004/2/16

N2 - Using existing, forward-in-time integration schemes, we demonstrate that under certain conditions it is possible to compute the solution at earlier times, even in the presence of stiffness (for which reverse integration is unstable). This technique can be used when a reverse integrator is not available - for example, when all one has is a forward-in-time legacy code. It can also be used for the "reverse coarse" integration of the macroscopic closure of a system defined by a microscopic model which itself is naturally forward in time (e.g., a particle model of a gas). The method proposed has stability properties that enable it to converge to stationary points of unstable stiff systems.

AB - Using existing, forward-in-time integration schemes, we demonstrate that under certain conditions it is possible to compute the solution at earlier times, even in the presence of stiffness (for which reverse integration is unstable). This technique can be used when a reverse integrator is not available - for example, when all one has is a forward-in-time legacy code. It can also be used for the "reverse coarse" integration of the macroscopic closure of a system defined by a microscopic model which itself is naturally forward in time (e.g., a particle model of a gas). The method proposed has stability properties that enable it to converge to stationary points of unstable stiff systems.

KW - Differential equations

KW - Reverse integration

KW - Stationary points

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SN - 0375-9601

VL - 321

SP - 335

EP - 343

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 5-6

ER -

Computing in the past with forward integration

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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