Randomized Runge–Kutta method — Stability and convergence under inexact information期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Randomized Runge–Kutta method — Stability and convergence under inexact information

Institution:	1. Univ. Limoges, CNRS, XLIM, UMR 7252, F-87000 Limoges, France;2. Université Grenoble Alpes, Laboratoire Jean Kuntzmann, CNRS, UMR 5224, 700 avenue centrale, IMAG - CS 40700, 38058 Grenoble cedex 9, France;1. CNRS (UMI 3069, PIMS), Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, V5A 1S6, Canada;2. CNRS, École polytechnique, Institut Polytechnique de Paris, Laboratoire d''Informatique de l''École Polytechnique (LIX, UMR 7161), Bâtiment Alan Turing, CS35003, 1, rue Honoré d''Estienne d''Orves, 91120 Palaiseau, France;1. Dipartimento di Ingegneria Industriale, Università degli Studi di Firenze, Italy;2. Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Italy;3. Namur Center for Complex Systems (naXys), University of Namur, 61, rue de Bruxelles, B-5000 Namur, Belgium

Abstract:	We deal with optimal approximation of solutions of ODEs under local Lipschitz condition and inexact discrete information about the right-hand side functions. We show that the randomized two-stage Runge–Kutta scheme is the optimal method among all randomized algorithms based on standard noisy information. We perform numerical experiments that confirm our theoretical findings. Moreover, for the optimal algorithm we rigorously investigate properties of regions of absolute stability.

Keywords:	Noisy information Randomized Runge–Kutta algorithm Minimal error Mean-square stability Asymptotic stability Stability in probability
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