1. Composition Methods for Dynamical Systems Separable into Three Parts
- Author
-
Fernando Casas and Alejandro Escorihuela-Tomàs
- Subjects
composition methods ,Dynamical systems theory ,General Mathematics ,splitting methods ,010103 numerical & computational mathematics ,01 natural sciences ,Separable space ,Computer Science (miscellaneous) ,FOS: Mathematics ,Initial value problem ,Applied mathematics ,Mathematics - Numerical Analysis ,0101 mathematics ,Engineering (miscellaneous) ,Composition methods ,Mathematics ,geometric numerical integrators ,systems separable into three parts ,lcsh:Mathematics ,Numerical Analysis (math.NA) ,lcsh:QA1-939 ,Numerical integration ,010101 applied mathematics ,Improved performance ,Ordinary differential equation - Abstract
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a way that each part is explicitly solvable. The methods are obtained by applying different optimization criteria and preserve geometric properties of the continuous problem by construction. Different numerical examples exhibit their improved performance with respect to previous splitting methods in the literature.
- Published
- 2020