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Symbolic Method for Solving Nonlocal Boundary Value Problems for Systems of Ordinary Loaded Integro-Differential Equations

Author

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  • Efthimios Providas

    (Department of Environmental Sciences, University of Thessaly, Gaiopolis Campus, 415 00 Larissa, Greece)

  • Ioannis N. Parasidis

    (Department of Environmental Sciences, University of Thessaly, Gaiopolis Campus, 415 00 Larissa, Greece)

  • Jeyhun E. Musayev

    (Department of Mechanics, Azerbaijan University of Architecture and Construction, Ayna Sultanova 11, AZ1073 Baku, Azerbaijan)

Abstract

A symbolic method is presented for examining the solvability and constructing the exact solution to boundary value problems for systems of linear ordinary loaded differential equations and loaded integro-differential equations with nonlocal boundary conditions. The method uses the inverse of the differential operator involved in the system of loaded differential or integro-differential equations. A solvability criterion based on the determinant of a matrix and an exact analytical matrix-form solution formula are presented. For the implementation of the method into computer algebra system software, two algorithms are provided. The effectiveness of the method is demonstrated by solving several problems. The theoretical and practical results obtained complement the existing literature on the subject.

Suggested Citation

  • Efthimios Providas & Ioannis N. Parasidis & Jeyhun E. Musayev, 2026. "Symbolic Method for Solving Nonlocal Boundary Value Problems for Systems of Ordinary Loaded Integro-Differential Equations," Mathematics, MDPI, vol. 14(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:7:p:1128-:d:1908179
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