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How one can repair non-integrable Kahan discretizations
- Source :
- J. Phys. A: Math. Theor., 2020, 53, 37LT01, 7 pp
- Publication Year :
- 2020
-
Abstract
- Kahan discretization is applicable to any system of ordinary differential equations on $\mathbb R^n$ with a quadratic vector field, $\dot{x}=f(x)=Q(x)+Bx+c$, and produces a birational map $x\mapsto \widetilde{x}$ according to the formula $(\widetilde{x}-x)/\epsilon=Q(x,\widetilde{x})+B(x+\widetilde{x})/2+c$, where $Q(x,\widetilde{x})$ is the symmetric bilinear form corresponding to the quadratic form $Q(x)$. When applied to integrable systems, Kahan discretization preserves integrability much more frequently than one would expect a priori, however not always. We show that in some cases where the original recipe fails to preserve integrability, one can adjust coefficients of the Kahan discretization to ensure its integrability.<br />Comment: 6 pp
- Subjects :
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Phys. A: Math. Theor., 2020, 53, 37LT01, 7 pp
- Publication Type :
- Report
- Accession number :
- edsarx.2003.12596
- Document Type :
- Working Paper