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Two-Sided Approximation of Solutions of a Multipoint Problem for an Ordinary Differential Equation with Parameters

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Abstract

We construct an algorithm for the two-sided approximation of a solution of a multipoint boundary-value problem for a quasilinear differential equation under assumptions that are two-sided analogs of the Pokornyi B-monotonicity of the right-hand side of the equation. We establish conditions for the monotonicity of successive approximations and their uniform convergence to a solution of the problem.

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Authors and Affiliations

  1. “L’vivs’ka Politekhnika” National University, Lviv, Ukraine

    S. M. Mentyns’kyi

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  1. S. M. Mentyns’kyi
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 125–130, January, 2005.

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Mentyns’kyi, S.M. Two-Sided Approximation of Solutions of a Multipoint Problem for an Ordinary Differential Equation with Parameters. Ukr Math J 57, 149–156 (2005). https://doi.org/10.1007/s11253-005-0177-8

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  • DOI: https://doi.org/10.1007/s11253-005-0177-8

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