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On the Solution of Boundary Value Problems for Ordinary Differential Equations of Order n and 2n with General Boundary Conditions

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Computational Mathematics and Variational Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 159))

Abstract

We present a method for examining the existence and uniqueness and obtaining the exact solution to boundary value problems consisting of the differential equation Au = f, where A is a linear ordinary differential operator of order n, and multipoint and integral boundary conditions. We also derive a formula for computing the exact solution to even order boundary value problems encompassing the differential equation A 2u = f subject to 2n general boundary conditions. The method is based on the correct extensions of operators in Banach spaces.

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Authors and Affiliations

  1. University of Thessaly, Gaiopolis, Larissa, Greece

    I. N. Parasidis, E. Providas & S. Zaoutsos

Authors
  1. I. N. Parasidis
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  2. E. Providas
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  3. S. Zaoutsos
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Corresponding author

Correspondence to E. Providas .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Parasidis, I.N., Providas, E., Zaoutsos, S. (2020). On the Solution of Boundary Value Problems for Ordinary Differential Equations of Order n and 2n with General Boundary Conditions. In: Daras, N., Rassias, T. (eds) Computational Mathematics and Variational Analysis. Springer Optimization and Its Applications, vol 159. Springer, Cham. https://doi.org/10.1007/978-3-030-44625-3_17

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