Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776736 | Applied Numerical Mathematics | 2017 | 17 Pages |
Abstract
In this paper, multi-step Runge-Kutta-Nyström methods for the numerical integration of special second-order initial value problems are proposed and studied. These methods include classical Runge-Kutta-Nyström methods as special cases. General order conditions are derived by using the theory of B-series based on the set of special Nyström-trees, and two explicit methods with order five and six, respectively, are constructed. Numerical results show that our new methods are more efficient in comparison with classical Runge-Kutta-Nyström methods and other well-known high quality methods proposed in the scientific literature.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Jiyong Li, Xianfen Wang,