Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems Article Swipe

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Mathematics Dissipative system Differentiable function Lyapunov function Nabla symbol Exponential function Matrix (chemical analysis) Scheme (mathematics) Applied mathematics Skew-symmetric matrix Mathematical analysis Pure mathematics Symmetric matrix Square matrix Physics Quantum mechanics Composite material Eigenvalues and eigenvectors Nonlinear system Omega Materials science

Yuwen Li , Xinyuan Wu ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1137/15m1023257 · OA: W2472333466

In this paper, combining the ideas of exponential integrators and discrete gradients, we propose and analyze a new structure-preserving exponential scheme for the conservative or dissipative system $\dot{y} = Q(M y + \nabla U (y))$, where $Q$ is a $d\times d$ skew-symmetric or negative semidefinite real matrix, $M$ is a $d\times d$ symmetric real matrix, and $U : \mathbb{R}^d\rightarrow\mathbb{R}$ is a differentiable function. We present two properties of the new scheme. The paper is accompanied by numerical results that demonstrate the remarkable superiority of our new scheme in comparison with other structure-preserving schemes in the scientific literature.