A mathematical theory for numerical treatment of nonlinear two-point boundary value problems. (English summary) Japan J. Indust. Appl. Math. 23 (2006), no. 1, 31–62. The paper studies the two-point boundary value problem − ( p (x) u ′) ′ + f x, u, u ′ ) = 0, a ≤ x ≤ b, α0u (a) − α1u ′ (a) = α, β0u (b) − β1u ′ (b) = β. It provides: 1. Existence and uniqueness of the solution u. 2. A companion discrete boundary value problem with existence and uniqueness of its solution Ui. 3. The error |ui − Ui | up to second-order accuracy in mesh size. The embodied results improve some of the earlier ones. The paper is very well written and will be useful for theoretical as well as for applied research
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