The so-called structural methods for systems of partitioned ordinary differential equations studied by Olemskoy are considered. An ODE system partitioning is based on special structure of right-hand side dependencies on the unknown functions. The methods are generalization of Runge–Kutta–Nyström methods and as the latter are more efficient than classical Runge–Kutta schemes for a wide range of systems. Polynomial interpolants for structural methods that can be used for dense output and in standard approach to solve delay differential equations are constructed. The proposed methods take fewer stages than the existing most general continuous Runge–Kutta methods. The orders of the constructed methods are checked with constant step integration of test delay differential equations. Also the global error to computational costs ratios are compared for new and known methods by solving the problems with variable time-step.
CITATION STYLE
Eremin, A. S., & Kovrizhnykh, N. A. (2017). Continuous extensions for structural runge–kutta methods. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10405, pp. 363–378). Springer Verlag. https://doi.org/10.1007/978-3-319-62395-5_25
Mendeley helps you to discover research relevant for your work.