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Title: The numerical solution of boundary-value problems for differential equations with state dependent deviating arguments (English)
Author: Bakke, Vernon L.
Author: Jackiewicz, Zdzisław
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 34
Issue: 1
Year: 1989
Pages: 1-17
Summary lang: English
Category: math
Summary: A numerical method for the solution of a second order boundary value problem for differential equation with state dependent deviating argument is studied. Second-order convergence is established and a theorem about the asymptotic expansion of global discretization error is given. This theorem makes it possible to improve the accuracy of the numerical solution by using Richardson extrapolation which results in a convergent method of order three. This is in contrast to boundary value problems for ordinary differential equations where the use of Richardson extrapolation results in a method of order four. (English)
Keyword: second order
Keyword: difference operator
Keyword: second order convergence
Keyword: asymptotic expansion
Keyword: global discretization error
Keyword: numerical examples
Keyword: boundary value problem
Keyword: deviating argument
Keyword: Richardson extrapolation
Keyword: convergence of higher order
MSC: 34K10
MSC: 65L10
idZBL: Zbl 0669.65065
idMR: MR0982339
DOI: 10.21136/AM.1989.104330
Date available: 2008-05-20T18:35:47Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] V. L. Bakke Z. Jackiewicz: A note on the numerical computation of solutions to second order boundary value problems with state dependent deviating arguments.University of Arkansas Numerical Analysis Technical Report 65110-1, June, 1985.
Reference: [2] B. Chartres R. Stepleman: Convergence of difference methods for initial and boundary value problems with discontinuous data.Math. Соmр., v. 25, 1971, pp. 724-732. MR 0303739
Reference: [3] P. Chocholaty L. Slahor: A numerical method to boundary value problems for second order delay-differential equations.Numer. Math., v. 33, 1979, pp. 69-75. MR 0545743, 10.1007/BF01396496
Reference: [4] K. De Nevers K. Schmitt: An application of the shooting method to boundary value problems for second order delay equations.J. Math. Anal. Appl., v. 36, 1971, pp. 588-597. MR 0298166, 10.1016/0022-247X(71)90041-2
Reference: [5] L. J. Grimm K. Schmitt: Boundary value problems for delay-differential equations.Bull. Amer. Math. Soc., v. 74, 1968, pp. 997-1000. MR 0228785, 10.1090/S0002-9904-1968-12114-7
Reference: [6] L. J. Grimm K. Schmitt: Boundary value problems for differential equations with deviating arguments.Aequationes Math., v. 4, 1970, p. 176-190. MR 0262632, 10.1007/BF01817758
Reference: [7] G. A. Kamenskii S. B. Norkin L. E. Eľsgoľts: Some directions of investigation on the theory of differential equations with deviating arguments.(Russian). Trudy Sem. Tear. Diff. Urav. Otklon. Arg., v. 6, pp. 3-36.
Reference: [8] H. B. Keller: Numerical methods for two-point boundary-value problems.Blaisdel Publishing Company, Waltham 1968. Zbl 0172.19503, MR 0230476


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