Randomized Runge-Kutta method - Stability and convergence under inexact information

Bochacik Tomasz; Gocwin Maciej; Morkisz Pawel M.; Przybylowicz Pawel

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Randomized Runge-Kutta method - Stability and convergence under inexact information

机译：随机速率-Kutta方法 - 不精确信息下的稳定性和收敛性

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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. (C) 2021 Elsevier Inc. All rights reserved.

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《Journal of complexity》 |2021年第8期|101554.1-101554.21|共21页
作者
Bochacik Tomasz; Gocwin Maciej; Morkisz Pawel M.; Przybylowicz Pawel;
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AGH Univ Sci & Technol Fac Appl Math Al A Mickiewicza 30 PL-30059 Krakow Poland;

AGH Univ Sci & Technol Fac Appl Math Al A Mickiewicza 30 PL-30059 Krakow Poland;

AGH Univ Sci & Technol Fac Appl Math Al A Mickiewicza 30 PL-30059 Krakow Poland;

AGH Univ Sci & Technol Fac Appl Math Al A Mickiewicza 30 PL-30059 Krakow Poland;

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正文语种 eng
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关键词
Noisy information; Randomized Runge-Kutta algorithm; Minimal error; Mean-square stability; Asymptotic stability; Stability in probability;

机译：嘈杂的信息;随机跑步-Kutta算法;最小误差;均方稳定性;渐近稳定性;概率稳定性;

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Randomized Runge-Kutta method - Stability and convergence under inexact information

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