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Kahan introduced an explicit method of discretization for systems of firstorder differential equations with nonlinearities of degree at most two(quadratic vector fields). Kahan's method has attracted much interest due tothe fact that it preserves many of the geometrical properties of the originalcontinuous system. In particular, a large number of Hamiltonian systems ofquadratic vector fields are known for which their Kahan discretization is adiscrete integrable system. In this note, we introduce a special class ofexplicit order-preserving discretization schemes that are appropriate forcertain systems of ordinary differential equations of higher order and higherdegree.

Analogues of Kahan's method for higher order equations of higher degree