Exponential Average-Vector-Field Integrator for Conservative or Dissipative Systems

Xinyuan Wu () and Bin Wang
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Xinyuan Wu: Nanjing University, Department of Mathematics
Bin Wang: Qufu Normal University, School of Mathematical Sciences

Chapter Chapter 2 in Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, 2018, pp 29-53 from Springer

Abstract: Abstract This chapter focuses on discrete gradient integrators intending to preserve the first integral or the Lyapunov function of the original continuous system. Incorporating the discrete gradients with exponential integrators, we discuss a novel exponential integrator for the conservative or dissipative system $$\dot{y}=Q(My+\nabla U(y))$$ , where Q is a $$d\times d$$ real matrix, M is a $$d\times d$$ symmetric real matrix and $$U : \mathbb {R}^{d}\rightarrow \mathbb {R}$$ is a differentiable function. For conservative systems, the exponential integrator preservesExponential average-vector-field integrator the energy, while for dissipative systems, the exponential integrator preserves the decaying property of the Lyapunov function. Two properties of the new scheme are presented. Numerical experiments demonstrate the remarkable superiority of the new scheme in comparison with other structure-preserving schemes in the recent literature.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-9004-2_2

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DOI: 10.1007/978-981-10-9004-2_2

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