Rooted tree analysis of Runge--Kutta methods with exact treatment of linear terms
The author's aim is to provide a mathematical foundation of the methods called ETD Runge-Kutta, already proposed in literature. The main feature of these methods is that they treat exactly the linear terms of an ordinary differential equation, while the other terms are numerically integrated by a one-step method. The author assumes the point of view of Runge-Kutta methods, using a Butcher-like tableaux, whose elements are themselves matrices instead of scalar; then he applies the rooted tree analysis. Several classes of formulas are derived. The study of these methods is complete and well-detailed.
scientific article; zbMATH DE number 2164843
scientific article