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Exponential Integrators Based on Discrete Gradients for Linearly Damped/Driven Poisson Systems

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Abstract

Exponential integrators based on discrete gradient methods are applied to non-canonical Hamiltonian systems with added linear forcing/damping terms, which may be time-dependent. Changes in the dynamics, such as conservation of energy or Casimirs, which result from inclusion of the linear forcing/damping terms, are not exactly preserved by standard discrete gradient methods. However, those changes are shown to be exactly preserved by the exponential integrators in special circumstances. The methods are also symmetric, second order, and linearly stable. To demonstrate advantages in both accuracy and efficiency over other standard methods, the exponential integrators are applied to a three dimensional Lotka-Volterra system and a damped/driven Ablowitz-Ladik system.

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Acknowledgements

The author thanks Elena Celledoni, Brynjulf Owren, and Reinout Quispel for helpful conversations as the ideas in this article were being developed.

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  1. University of Central Florida, Orlando, USA

    Brian E. Moore

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  1. Brian E. Moore
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Moore, B.E. Exponential Integrators Based on Discrete Gradients for Linearly Damped/Driven Poisson Systems. J Sci Comput 87, 56 (2021). https://doi.org/10.1007/s10915-021-01468-1

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