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A class of robust numerical methods for solving dynamical systems with multiple time scales

Hou, Thomas Y. and Wang, Zhongjian and Zhang, Zhiwen (2019) A class of robust numerical methods for solving dynamical systems with multiple time scales. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200122-143531561

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Abstract

In this paper, we develop a class of robust numerical methods for solving dynamical systems with multiple time scales. We first represent the solution of a multiscale dynamical system as a transformation of a slowly varying solution. Then, under the scale separation assumption, we provide a systematic way to construct the transformation map and derive the dynamic equation for the slowly varying solution. We also provide the convergence analysis of the proposed method. Finally, we present several numerical examples, including ODE system with three and four separated time scales to demonstrate the accuracy and efficiency of the proposed method. Numerical results verify that our method is robust in solving ODE systems with multiple time scale, where the time step does not depend on the multiscale parameters.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1909.04289arXivDiscussion Paper
ORCID:
AuthorORCID
Zhang, Zhiwen0000-0002-3123-8885
Additional Information:The research of T. Hou is partially supported by the NSF Grants DMS-1613861, DMS-1907977, and DMS-1912654. The research Z. Wang is partially supported by the Hong Kong PhD Fellowship Scheme. The research of Z. Zhang is supported by Hong Kong RGC grants (Projects 27300616, 17300817, and 17300318), National Natural Science Foundation of China via grant 11601457, Seed Funding Programme for Basic Research (HKU), and Basic Research Programme (JCYJ20180307151603959) of The Science, Technology and Innovation Commission of Shenzhen Municipality. The computations were performed using the HK ITS research computing facilities that are supported in part by the Hong Kong UGC Special Equipment Grant (SEG HKU09).
Funders:
Funding AgencyGrant Number
NSFDMS-1613861
NSFDMS-1907977
NSFDMS-1912654
University of Hong KongUNSPECIFIED
Research Grants Council of Hong Kong27300616
Research Grants Council of Hong Kong17300817
Research Grants Council of Hong Kong17300318
National Natural Science Foundation of China11601457
Science, Technology and Innovation Commission of Shenzhen MunicipalityJCYJ20180307151603959
Hong Kong University Grants CommitteeSEG HKU09
Subject Keywords:Hamiltonian dynamical system; multiple time scales; stiff equations; convergence analysis; uniform accuracy; composition maps
Classification Code:AMS subject classifications: 34E13, 65L04, 65P10, 65L20
Record Number:CaltechAUTHORS:20200122-143531561
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200122-143531561
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100852
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:22 Jan 2020 23:05
Last Modified:22 Jan 2020 23:05

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