New classes of quadratic vector fields admitting integral-preserving Kahan-Hirota-Kimura discretizations
arXiv:1610.0366415 citationsh-index: 15
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This work extends the class of systems for which structure-preserving discretizations are known, offering potential benefits for numerical simulations in dynamics.
The paper identifies new families of quadratic vector fields whose Kahan-Hirota-Kimura discretization preserves conserved quantities and invariant measures from the continuous system, even when the original system is not integrable.
We present some new families of quadratic vector fields, not necessarily integrable, for which their Kahan-Hirota-Kimura discretization exhibits the preservation of some of the characterizing features of the underlying continuous systems (conserved quantities and invariant measures).