Multiple Richardson Extrapolation Applied to Explicit Runge–Kutta Methods

Autor:	Ágnes Havasi, Teshome Bayleyegn
Rok vydání:	2020
Předmět:	Runge–Kutta methods Differential equation Generalization High Energy Physics::Lattice Numerical analysis Two step Extrapolation Applied mathematics Richardson extrapolation Linear combination Mathematics
Zdroj:	Advances in High Performance Computing ISBN: 9783030553463 HPC
DOI:	10.1007/978-3-030-55347-0_22
Popis:	Richardson extrapolation has long been used to enhance the accuracy of time integration methods for solving differential equations. The original version of Richardson extrapolation is based on a suitable linear combination of numerical solutions obtained by the same numerical method with two different time-step sizes. This procedure can be extended to more than two step sizes in a natural way, and the resulting method is called repeated Richardson extrapolation. In this talk we investigate another possible generalization of the idea of Richardson extrapolation, where the extrapolation is applied to the combination of some underlying method and the classical Richardson extrapolation. The procedure obtained in this way, called multiple Richardson extrapolation, is analysed for accuracy and absolute stability when combined with some explicit Runge–Kutta methods.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d75ea627a183a4b4244543b129a719a9 https://doi.org/10.1007/978-3-030-55347-0_22 Zobrazit plný text záznamu