A new high precision energy-preserving integrator for system of oscillatory second-order differential equations

Bin Wang; Xinyuan Wu

doi:10.1016/j.physleta.2012.02.040

A new high precision energy-preserving integrator for system of oscillatory second-order differential equations

Bin Wang
, Xinyuan Wu

Nanjing University

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

57 Scopus citations

Abstract

This Letter proposes a new high precision energy-preserving integrator for system of oscillatory second-order differential equations ^q″(t) +Mq(t)=f(q(t)) with a symmetric and positive semi-definite matrix M and f(q)=-∇U(q). The system is equivalent to a separable Hamiltonian system with Hamiltonian H(p,q)=12^pTp+12^qTMq+U(q). The properties of the new energy-preserving integrator are analyzed. The well-known Fermi-Pasta-Ulam problem is performed numerically to show that the new integrator preserves the energy integral with higher accuracy than Average Vector Field (AVF) method and an energy-preserving collocation method.

Original language	English
Pages (from-to)	1185-1190
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	376
Issue number	14
DOIs	https://doi.org/10.1016/j.physleta.2012.02.040
State	Published - 5 Mar 2012
Externally published	Yes

Keywords

Energy-preserving integrators
Fermi-Pasta-Ulam problem
Hamiltonian systems
Oscillatory differential equations

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10.1016/j.physleta.2012.02.040

Cite this

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title = "A new high precision energy-preserving integrator for system of oscillatory second-order differential equations",

abstract = "This Letter proposes a new high precision energy-preserving integrator for system of oscillatory second-order differential equations q″(t) +Mq(t)=f(q(t)) with a symmetric and positive semi-definite matrix M and f(q)=-∇U(q). The system is equivalent to a separable Hamiltonian system with Hamiltonian H(p,q)=12pTp+12qTMq+U(q). The properties of the new energy-preserving integrator are analyzed. The well-known Fermi-Pasta-Ulam problem is performed numerically to show that the new integrator preserves the energy integral with higher accuracy than Average Vector Field (AVF) method and an energy-preserving collocation method.",

keywords = "Energy-preserving integrators, Fermi-Pasta-Ulam problem, Hamiltonian systems, Oscillatory differential equations",

author = "Bin Wang and Xinyuan Wu",

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doi = "10.1016/j.physleta.2012.02.040",

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T1 - A new high precision energy-preserving integrator for system of oscillatory second-order differential equations

AU - Wang, Bin

AU - Wu, Xinyuan

PY - 2012/3/5

Y1 - 2012/3/5

N2 - This Letter proposes a new high precision energy-preserving integrator for system of oscillatory second-order differential equations q″(t) +Mq(t)=f(q(t)) with a symmetric and positive semi-definite matrix M and f(q)=-∇U(q). The system is equivalent to a separable Hamiltonian system with Hamiltonian H(p,q)=12pTp+12qTMq+U(q). The properties of the new energy-preserving integrator are analyzed. The well-known Fermi-Pasta-Ulam problem is performed numerically to show that the new integrator preserves the energy integral with higher accuracy than Average Vector Field (AVF) method and an energy-preserving collocation method.

AB - This Letter proposes a new high precision energy-preserving integrator for system of oscillatory second-order differential equations q″(t) +Mq(t)=f(q(t)) with a symmetric and positive semi-definite matrix M and f(q)=-∇U(q). The system is equivalent to a separable Hamiltonian system with Hamiltonian H(p,q)=12pTp+12qTMq+U(q). The properties of the new energy-preserving integrator are analyzed. The well-known Fermi-Pasta-Ulam problem is performed numerically to show that the new integrator preserves the energy integral with higher accuracy than Average Vector Field (AVF) method and an energy-preserving collocation method.

KW - Energy-preserving integrators

KW - Fermi-Pasta-Ulam problem

KW - Hamiltonian systems

KW - Oscillatory differential equations

UR - https://www.scopus.com/pages/publications/84862782915

U2 - 10.1016/j.physleta.2012.02.040

DO - 10.1016/j.physleta.2012.02.040

M3 - 文章

AN - SCOPUS:84862782915

SN - 0375-9601

VL - 376

SP - 1185

EP - 1190

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

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

IS - 14

ER -

A new high precision energy-preserving integrator for system of oscillatory second-order differential equations

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Keywords

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