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 INTEGRABLE DISCRETISATION OF THE LOTKA-VOLTERRA SYSTEM He, Yang1,2,3; Sun, Yajuan4; Shang, Zaijiu5 2015 Source Publication JOURNAL OF COMPUTATIONAL MATHEMATICS ISSN 0254-9409 Volume 33Issue:5Pages:468-494 Abstract In this paper, we apply Hirota's discretisation to a three-dimensional integrable Lotka-Volterra system. By analyzing the three-dimensional modified equation of the resulting numerical method, we show that it is volume-preserving, and has two independent first integrals. Moreover, it can be formally reduced to a system in one dimension via a volume-preserving transformation. If the given initial value is located in the positive octant, we prove that the numerical solution is confined to a one-dimensional connected and compact space which is diffeomorphic to a circle. Keyword Integrable Lotka-Volterra system Hirota's integrable discretisation Backward error analysis Modified differential equation DOI 10.4208/jcm.1504-m4543 Language 英语 Funding Project Fundamental Research Funds for the Central Universities[WK2030040057] ; National Natural Science Foundation of China[11271357] ; Foundation for Innovative Research Groups of the NNSFC[11321061] ; ITER-China Program[2014G-B124005] ; Foundation of the NNSFC[10990012] ; Marine Public Welfare Project of China[201105032] WOS Research Area Mathematics WOS Subject Mathematics, Applied ; Mathematics WOS ID WOS:000365413300002 Publisher GLOBAL SCIENCE PRESS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/21364 Collection 计算数学与科学工程计算研究所数学所 Affiliation 1.Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China2.Univ Sci & Technol China, Collaborat Innovat Ctr Adv Fus Energy & Plasma Sc, Hefei 230026, Anhui, Peoples R China3.Chinese Acad Sci, Univ Sci & Technol China, Key Lab Geospace Environm, Hefei 230026, Anhui, Peoples R China4.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China5.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China Recommended CitationGB/T 7714 He, Yang,Sun, Yajuan,Shang, Zaijiu. INTEGRABLE DISCRETISATION OF THE LOTKA-VOLTERRA SYSTEM[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2015,33(5):468-494. APA He, Yang,Sun, Yajuan,&Shang, Zaijiu.(2015).INTEGRABLE DISCRETISATION OF THE LOTKA-VOLTERRA SYSTEM.JOURNAL OF COMPUTATIONAL MATHEMATICS,33(5),468-494. MLA He, Yang,et al."INTEGRABLE DISCRETISATION OF THE LOTKA-VOLTERRA SYSTEM".JOURNAL OF COMPUTATIONAL MATHEMATICS 33.5(2015):468-494.
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