Browsing NTNU Open by Author "Quispel, Gilles Reinout Willem"
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Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation
van der Kamp, Peter H.; Celledoni, Elena; Mclachlan, Robert, i; McLaren, David I.; Owren, Brynjulf; Quispel, Gilles Reinout Willem (Peer reviewed; Journal article, 2019)Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation -
Using aromas to search for preserved measures and integrals in Kahan’s method
Bogfjellmo, Geir; Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf Rustad; Quispel, Gilles Reinout Willem (Peer reviewed; Journal article, 2023)The numerical method of Kahan applied to quadratic differential equations is known to often generate integrable maps in low dimensions and can in more general situations exhibit preserved measures and integrals. Computerized ... -
Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
Celledoni, Elena; Evripidou, Charalambos; McLaren, David I.; Owren, Brynjulf; Quispel, Gilles Reinout Willem; Tapley, Benjamin; van der Kamp, Peter H. (Peer reviewed; Journal article, 2019)In this letter we propose a systematic approach for detecting and calculating integrals and preserved measures of rational maps. The approach is based on the use of cofactors and discrete Darboux polynomials and relies on ...