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Modification of the Euler Polygonal Method for Solving a Semi-periodic Boundary Value Problem for Pseudo-parabolic Equation of Special Type

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Abstract

A semi-periodic boundary value problem for a pseudo-parabolic equation of special type is investigated. A modification of the Euler polygonal method is applied to a semi-periodic boundary-value problem for a non-classical differential equation of third order. By introducing new unknown functions, the problem under consideration is reduced to an equivalent problem consisting of a family of periodic boundary value problems for a system of two ordinary differential equations and some integral relations. We obtain the conditions for the unique solvability of the problem. The estimates of convergence of approximate solution of the equivalent problem to the exact solution of the original problem are established.

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Acknowledgements

The authors thank the referees for their careful reading of the manuscript and their thoughtful comments and efforts towards improving our manuscript.

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Authors and Affiliations

  1. Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, 125, Pushkin str., 050010, Almaty, Kazakhstan

    A. T. Assanova & S. S. Kabdrakhova

  2. Al-Farabi Kazakh National University, 71, Al-Farabi Ave., 050040, Almaty, Kazakhstan

    A. T. Assanova & S. S. Kabdrakhova

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  1. A. T. Assanova
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  2. S. S. Kabdrakhova
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Correspondence to A. T. Assanova.

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This investigation is supported by Grant of the Ministry Education and Science of the Republic of Kazakhstan, no. AP 05131220.

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Assanova, A.T., Kabdrakhova, S.S. Modification of the Euler Polygonal Method for Solving a Semi-periodic Boundary Value Problem for Pseudo-parabolic Equation of Special Type. Mediterr. J. Math. 17, 109 (2020). https://doi.org/10.1007/s00009-020-01540-4

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  • DOI: https://doi.org/10.1007/s00009-020-01540-4

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