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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

References:

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[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

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[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