We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and non-autonomous dynamical systems with conserved quantities of arbitrary forms, such as time-dependent conserved quantities. Sufficient conditions to construct conservative schemes of arbitrary order are derived using the multiplier method. General formulas for first-order conservative schemes are constructed using divided difference calculus. New conservative schemes are found for various dynamical systems such as Euler's equation of rigid body rotation, Lotka-Volterra systems, the planar restricted three-body problem and the damped harmonic oscillator.
Conservative and dissipative discretisations of multi-conservative ODEs and GENERIC systems
Mathematical Institute, University of Oxford（牛津大学数学研究所）；Mathematical Institute, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院数学研究所）
Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: A study using POD-Galerkin and dynamical low rank approximation
Mass Conservative and Energy Stable Finite Difference Methods for the Quasi-incompressible Navier-Stokes-Cahn-Hilliard system: Primitive Variable and Projection-Type Schemes
University of California, Irvine（加州大学尔湾分校）；University of Dundee（邓迪大学）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
