 A note on continuous-stage Runge–Kutta methodsWensheng Tang Applied Mathematics and Computation, 2018, vol. 339, issue C, 231-241 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 associated with order conditions. In this note, we will review, discuss and further promote the recently-developed csRK theory. In particular, we will place emphasis on geometric integrators including symplectic methods, symmetric methods and energy-preserving methods which play a central role in the field of geometric numerical integration. Keywords: Continuous-stage Runge–Kutta methods; Hamiltonian systems; Symplectic methods; Conjugate-symplectic methods; Energy-preserving methods; Symmetric methods (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:231-241 DOI: 10.1016/j.amc.2018.07.044 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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