Geometric and integrability properties of Kahan's method

2018/05/22 by Elena Celledoni, Celledoni, Elena, David McLaren +5
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1805.08382

openalex publication_date 2018/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a quadratic vector field on ℝⁿ possessing a quadratic first integral depending on two of the independent variables, we give a constructive proof that Kahan's discretization method exactly preserves a nearby modifed integral. Building on this result, we present a family of integrable quadratic vector fields (including the Euler top) whose Kahan discretization is a novel 10-parameter family of integrable maps.

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