TY - JOUR

T1 - Computing in the past with forward integration

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

UR - http://www.scopus.com/inward/record.url?scp=1042300990&partnerID=8YFLogxK

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U2 - 10.1016/j.physleta.2003.12.041

DO - 10.1016/j.physleta.2003.12.041

M3 - Article

AN - SCOPUS:1042300990

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

SN - 0375-9601

IS - 5-6

ER -