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Titolo:
Computational uncertainty principle in nonlinear ordinary differential equations - II. Theoretical analysis
Autore:
Li, JP; Zeng, QC; Chou, JF;
Indirizzi:
Chinese Acad Sci, State Key Lab Numer Modelling Atmospher Sci & Geo, Inst Atmospher Phys, Beijing 100029, Peoples R China Chinese Acad Sci Beijing Peoples R China 100029 100029, Peoples R China Lanzhou Univ, Dept Atmospher Sci, Lanzhou 730000, Peoples R China Lanzhou Univ Lanzhou Peoples R China 730000 zhou 730000, Peoples R China
Titolo Testata:
SCIENCE IN CHINA SERIES E-TECHNOLOGICAL SCIENCES
fascicolo: 1, volume: 44, anno: 2001,
pagine: 55 - 74
SICI:
2095-0624(200102)44:1<55:CUPINO>2.0.ZU;2-3
Fonte:
ISI
Lingua:
ENG
Keywords:
computational uncertainty principle; round-off error; discretization enter; universal relation; machine precision; maximally effective computation time (MECT); optimal stepsize (OS); convergence;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Engineering, Computing & Technology
Citazioni:
12
Recensione:
Indirizzi per estratti:
Indirizzo: Li, JP Chinese Acad Sci, State Key Lab Numer Modelling Atmospher Sci & Geo, Inst Atmospher Phys, Beijing 100029, Peoples R China Chinese Acad Sci Beijing Peoples R China 100029 , Peoples R China
Citazione:
J.P. Li et al., "Computational uncertainty principle in nonlinear ordinary differential equations - II. Theoretical analysis", SCI CHINA E, 44(1), 2001, pp. 55-74

Abstract

The error propagation for general numerical method in ordinary differential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components of round-off error occurring in floating-point computation are fully detailed. By introducing a new kind of recurrent inequality, the classical error bounds for linear multistep methods are essentially improved, and joining probabilistic theory the "normal" growth of accumulated round-off error is derived. Moreover, a unified estimate for the total error of general method is given. On the basis of these results, we rationally interpret the various phenomena found in the numerical experiments in part I of this paper and derive two universal relations which are independent of types of ODEs, initial values and numerical schemes and are consistent with the numerical results. Furthermore, we give the explicitly mathematical expression of the computational uncertainty principle and expound the intrinsic relation between two uncertainties which result from the inaccuracies of numerical method and calculating machine.

ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 29/03/20 alle ore 15:29:45