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Method for studying boundary value problems with nonlinear boundary conditions

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Ukrainian Mathematical Journal Aims and scope

Abstract

A constructive approach to the determination of an approximate solution of a boundary value problem with nonlinear boundary conditions g[z (0), z (T)]=0 is proposed. Existence of the exact solution is proved, and error estimates for the constructed approximate solution are provided.

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Literature cited

  1. A. M. Samoilenko and I. I. Ronto, Numerical-analytical Methods of Study of Solutions of Boundary Value Problems [in Russian], Naukova Dumka, Kiev (1986).

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  2. M. Urabe, “Galerkin procedures for nonlinear periodic systems,” Arch. Rat. Mech. Anal.,20, No. 2, 120–152 (1965).

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Authors and Affiliations

  1. Mathematics Institute, Academy of Sciences of the Ukrainian SSR, Kiev University, Kiev

    A. M. Samoilenko & Le Lyiong Tai

Authors
  1. A. M. Samoilenko
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  2. Le Lyiong Tai
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 951–957, July, 1990.

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Samoilenko, A.M., Tai, L.L. Method for studying boundary value problems with nonlinear boundary conditions. Ukr Math J 42, 844–850 (1990). https://doi.org/10.1007/BF01062089

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  • DOI: https://doi.org/10.1007/BF01062089

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