Geometric and integrability properties of Kahan's method: the preservation of certain quadratic integrals

被引：12

作者：

Celledoni, E. ^{[1
]}

McLaren, D., I ^{[2
]}

Owren, B. ^{[1
]}

Quispel, G. R. W. ^{[2
]}

机构：

[1] NTNU, Dept Math Sci, N-7491 Trondheim, Norway

[2] La Trobe Univ, Dept Math, Bundoora, Vic 3083, Australia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2019年 / 52卷 / 06期

基金：

欧盟地平线“2020”; 澳大利亚研究理事会;

关键词：

integrability; discretization; ordinary differential equations; DISCRETIZATION;

D O I：

10.1088/1751-8121/aafb1e

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Given a quadratic vector field on R-n 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 modified integral. Building on this result, we present a family of integrable quadratic vector fields (including the Euler top) whose Kahan discretization is a family of integrable maps.

引用

页数：9

共 8 条

[1] Integrability properties of Kahan's method
Celledoni, Elena
McLachlan, Robert I.
McLaren, David I.
Owren, Brynjulf
Quispel, G. R. W.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (36)
[2] Geometric properties of Kahan's method
Celledoni, Elena
McLachlan, Robert I.
Owren, Brynjulf
Quispel, G. R. W.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2013, 46 (02)
[3] Some Integrability Properties of the Kahan Method
Zanna, Antonella
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2016 (ICNAAM-2016), 2017, 1863
[4] USING AROMAS TO SEARCH FOR PRESERVED MEASURES AND INTEGRALS IN KAHAN'S METHOD
Bogfjellmo, Geir
Celledoni, Elena
Mclachlan, Robert I.
Owren, Brynjulf
Quispel, G. R. W.
MATHEMATICS OF COMPUTATION, 2024, 93 (348) : 1633 - 1653
[5] The D-bar method, inversion of certain integrals and integrability in 4+2 and 3+1 dimensions
Fokas, A. S.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (34)
[6] Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method
Bizyaev, I. A.
Kozlov, V. V.
SBORNIK MATHEMATICS, 2015, 206 (12) : 1682 - 1706
[7] On the Influence of Certain Geometric Characteristics of the Resonator on the Impedance Determined by the Dean's Method
Palchikovskiy, Vadim
Khramtsov, Igor
Kustov, Oleg
ACOUSTICS, 2022, 4 (02): : 382 - 393
[8] The exponential integrability properties and strong convergence rate of an explicit Euler's method for highly nonlinear stochastic differential equations
Zhan, Weijun
Guo, Qian
He, Jie
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2024,

← 1 →