Trees and numerical methods for ordinary differential equations. (English) Zbl 1184.65072

Summary: 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.


65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
05C05 Trees
Full Text: DOI


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