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Geometric properties of Kahan's method

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In unpublished lecture notes of 1993, William Kahan proposed a numerical method for integrating ordinary differential equations that he called `unconventional’ which he reported had been delivering excellent results for more than 20 years. Interest in the method was revived when researchers showed that the method had an uncanny, and unexplained, ability to (sometimes) preserve integrability. Now Elena Celledoni, Brynjulf Owren, Reinout Quispel and myself have shown that the method is not, in fact, unconventional, but that its properties certainly are – they are novel for integrability, for Runge-Kutta methods, and for geometric integration simultaneously.

This talk is part of the Applied and Computational Analysis series.

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