najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2020-11-3-275-284najo-421Research ArticleMATHEMATICSМАТЕМАТИКАApproximate analytical method for finding eigenvalues of Sturm-Liouville problem with generalized boundary condition of the third kindLukyanovV. D.

Kondrat’evsky, 72, St. Petersburg, 195271

lukyanovvd@rambler.ruBulekbaevD. A.

Zhdanovskaya, 13, St. Petersburg, 197198

atiman@mail.ruMorozovA. V.

Zhdanovskaya, 13, St. Petersburg, 197198

alex.morozof@gmail.comNosovaL. V.

Zhdanovskaya, 13, St. Petersburg, 197198

lvn1201@gmail.comJoint-Stock Company “Avangard”Russian FederationMozhaisky Military Space AcademyRussian Federation202030072025113275–284Copyright © Lukyanov V.D., Bulekbaev D.A., Morozov A.V., Nosova L.V., 20252025Lukyanov V.D., Bulekbaev D.A., Morozov A.V., Nosova L.V.Lukyanov V.D., Bulekbaev D.A., Morozov A.V., Nosova L.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/421

The Sturm-Liouville problem is solved for a linear differential second-order equation with generalized boundary conditions of the third kind Generalized boundary conditions consist of a linear combination of the boundary values of a function and its derivative. The coefficients of the linear combination are polynomials of the boundary problem eigenvalue. A method of approximate analytical calculation of boundary problem eigenvalues is proposed The calculation error of an eigenvalue is estimated.

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The authors declare that there are no conflicts of interest present.