Abstract
This paper presents a review of the role played by trees in the theory of Runge–Kutta methods. The use of trees is in contrast to early publications on numerical methods, in which a deceptively simpler approach was used. This earlier approach is not only non-rigorous, but also incorrect. It is now known, for example, that methods can have different orders when applied to a single equation and when applied to a system of equations; the earlier approach cannot show this. Trees have a central role in the theory of Runge–Kutta methods and they also have applications to more general methods, involving multiple values and multiple stages.
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Butcher, J.C. Trees and numerical methods for ordinary differential equations. Numer Algor 53, 153–170 (2010). https://doi.org/10.1007/s11075-009-9285-0
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DOI: https://doi.org/10.1007/s11075-009-9285-0