How one can repair non-integrable Kahan discretizations
| العنوان: | How one can repair non-integrable Kahan discretizations |
|---|---|
| المؤلفون: | Matteo Petrera, René Zander, Yuri B. Suris |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Statistics and Probability, Pure mathematics, Discretization, Integrable system, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Symmetric bilinear form, 010102 general mathematics, FOS: Physical sciences, General Physics and Astronomy, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Quadratic form (statistics), 01 natural sciences, 010305 fluids & plasmas, Quadratic equation, Modeling and Simulation, Ordinary differential equation, 0103 physical sciences, Vector field, Exactly Solvable and Integrable Systems (nlin.SI), 0101 mathematics, Mathematical Physics, Mathematics |
| الوصف: | 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. Comment: 6 pp |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a3210f8853c37d93ff1981800f6cc665 http://arxiv.org/abs/2003.12596 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....a3210f8853c37d93ff1981800f6cc665 |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |