The numerical solution of boundary-value problems for differential equations with state dependent deviating arguments. (English) Zbl 0669.65065

This paper deals with a numerical solution of a second order boundary value problem with state dependent deviating argument. The presented method is obtained by approximating the second derivative by a second order difference operator and approximating the solutions at non-grid points by piecewise cubic interpolation. Second order convergence is established and a theorem about the asymptotic expansion of the global discretization error is given. The results are illustrated by some numerical examples.
Reviewer: P.Chocholatý


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34K10 Boundary value problems for functional-differential equations
Full Text: DOI EuDML


[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.
[2] B. Chartres R. Stepleman: Convergence of difference methods for initial and boundary value problems with discontinuous data. Math. Comp., v. 25, 1971, pp. 724-732. · Zbl 0244.65051 · doi:10.2307/2004339
[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. · Zbl 0432.65046 · doi:10.1007/BF01396496
[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. · Zbl 0219.34050 · doi:10.1016/0022-247X(71)90041-2
[5] L. J. Grimm K. Schmitt: Boundary value problems for delay-differential equations. Bull. Amer. Math. Soc., v. 74, 1968, pp. 997-1000. · Zbl 0167.38504 · doi:10.1090/S0002-9904-1968-12114-7
[6] L. J. Grimm K. Schmitt: Boundary value problems for differential equations with deviating arguments. Aequationes Math., v. 4, 1970, p. 176-190. · Zbl 0198.13201 · doi:10.1007/BF01817758
[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.
[8] H. B. Keller: Numerical methods for two-point boundary-value problems. Blaisdel Publishing Company, Waltham 1968. · Zbl 0172.19503
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.