A note on continuous-stage Runge-Kutta methods

Wensheng Tang

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arXiv · 1804.08575

A note on continuous-stage Runge-Kutta methods

Wensheng Tang

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Abstract

We provide a note on continuous-stage Runge-Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge-Kutta (RK) methods, can give us a new perspective on RK discretization and it may enlarge the application of RK approximation theory in modern mathematics and engineering fields. A highlighted advantage of investigation of csRK methods is that we do not need to study the tedious solution of multi-variable nonlinear algebraic equations stemming from order conditions. In this note, we will discuss and promote the recently-developed csRK theory. In particular, we will place emphasis on structure-preserving algorithms including symplectic methods, symmetric methods and energy-preserving methods which play a central role in the field of geometric numerical integration.

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Wensheng Tang. 2018-04-23. A note on continuous-stage Runge-Kutta methods. https://arxiv.org/abs/1804.08575

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