Article
Full entry |
PDF
(1.9 MB)
Feedback
PDF
(1.9 MB)
Feedback
Keywords:
second order; difference operator; second order convergence; asymptotic expansion; global discretization error; numerical examples; boundary value problem; deviating argument; Richardson extrapolation; convergence of higher order
second order; difference operator; second order convergence; asymptotic expansion; global discretization error; numerical examples; boundary value problem; deviating argument; Richardson extrapolation; convergence of higher order
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.
References:
[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. Соmр., v. 25, 1971, pp. 724-732. MR 0303739
[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. DOI 10.1007/BF01396496 | MR 0545743
[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. DOI 10.1016/0022-247X(71)90041-2 | MR 0298166
[5] L. J. Grimm K. Schmitt: Boundary value problems for delay-differential equations. Bull. Amer. Math. Soc., v. 74, 1968, pp. 997-1000. DOI 10.1090/S0002-9904-1968-12114-7 | MR 0228785
[6] L. J. Grimm K. Schmitt: Boundary value problems for differential equations with deviating arguments. Aequationes Math., v. 4, 1970, p. 176-190. DOI 10.1007/BF01817758 | MR 0262632
[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. MR 0230476 | Zbl 0172.19503
Search
Partner of
