Романюк Наталія Миколаївна

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12. Makarov V.L., Romaniuk N.M. & Bandyrskii B.I. (2020- reprint) Generalization of Resonant Equations for the Laguerre- and Legendre-Type Polynomials to Equations of the Fourth Order. Ukr. Math. J., Vol. 71, pp. 1751–1762, https://doi.org/10.1007/s11253-020-01745-6 (in English). Bandyrskii B. I., Makarov V. L., Romaniuk N. M. (2019) Generalization of resonance equations for the Laguerre- and Legendre-type polynomials to the fourth-order equations. Ukr. Mat. Zh., Vol. 71, No. 11, pp. 1529-1538 (in Ukrainian. English summary) Scopus


11. Makarov, V. & Romaniuk, N. (2019) Exponentially convergent symbolic algorithm of the functional-discrete method for the fourth order Sturm-Liouville problems with polynomial coefficients. Journal of Computational and Applied Mathematics, vol. 358, pp. 405-423, https://doi.org/10.1016/j.cam.2019.03.024, https://arxiv.org/abs/1806.09193 (in English) Scopus Web of Science


10. Makarov, V. & Romaniuk, N. (2018) Symbolic Algorithm of the Functional-Discrete Method for a Sturm–Liouville Problem with a Polynomial Potential. Computational Methods in Applied Mathematics, 18(4), pp. 703-715, doi:10.1515/cmam-2017-0040 (in English) Scopus Web of Science Publons


9.Gavrilyuk, I., Makarov, V. & Romaniuk, N. (2018) Super-Exponentially Convergent Parallel Algorithm for a Fractional Eigenvalue Problem of Jacobi-Type. Computational Methods in Applied Mathematics, 18(1), pp. 21-32, doi:10.1515/cmam-2017-0010 (in English) Scopus Web of Science Publons


8. Gavrilyuk, I.P., Makarov, V.L. & Romaniuk, N.M. (2017- reprint). Superexponentially convergent algorithm for an abstract eigenvalue problem with applications to ordinary differential equations. J. Math. Sci., Vol. 220, No.3, pp. 273-300, doi: 10.1007/s10958-016-3184-4. (2015) Nonlinear Oscillations, 18 (3), pp. 332-356, url: https://www.imath.kiev.ua/~nosc/web/show_article.php?article_id=1112&lang=en (in English) Scopus


7. Makarov, V.L. & Romanyuk, N.M. (2015) Super-exponential convergence of the FD-method for spectral problem in Banach space. Zb. Pr. Inst. Mat. NAN Ukr., Vol. 12, No. 5, pp. 109-131 (in Ukrainian. English summary).

6. Makarov, V.L. & Romaniuk, N.M. (2015) The FD-method for an eigenvalue problem in a case where the base problem has eigenvalues of arbitrary multiplicities in a Hilbert space. Reports of the National Academy of Sciences of Ukraine, No. 5, pp. 26-34, doi: 10.15407/dopovidi2015.05.026 (in Ukrainian. English summary).

5. Makarov, V.L., Romanyuk, N.M. & Lazurchak, I.I. (2014) FD-method for eigenvalue problem with multiple eigenvalues of the basic problem. Zb. Pr. Inst. Mat. NAN Ukr., Vol. 11, No. 4, 239--265 (in Ukrainian. English summary).

4. Makarov, V.L. & Romaniuk, N.M. (2014) New properties of the FD-method in its applications to the Sturm–Liouville problems, Reports of the National Academy of Sciences of Ukraine, No. 2, pp. 26–31, doi: 10.15407/dopovidi2014.02.026 (in Ukrainian. English summary).

3. Makarov V., Romaniuk N. & Lazurchak I. (2014) FD-method for solving the Sturm-Liouville problem with potential that is the derivative of a function of bounded variation. Journal of Numerical and Applied Mathematics, Vol. 116, No. 2, pp. 68–88, url: http://jnam.lnu.edu.ua/pdf/y2014_no2(116)_art06_makarov_romaniuk_lazurchak.pdf (in English). Web of Science Publons

2. Makarov, V.L. & Romaniuk, N.N. (2014) New implementation of the FD-method for Sturm–Liouville problems with Dirichlet–Neumann boundary conditions, Tr. Inst. Mat., Vol. 22, Is. 1, pp. 98–106, URL: http://mi.mathnet.ru/eng/timb211 (in Russian. English summary)

1. Makarov, V., Romanyuk, N. & Lazurchak, I. (2013) Experimental and analytical investigation of properties of FD-method components in its application to Sturm-Liouville problem. Zb. Pr. Inst. Mat. NAN Ukr. Vol. 10, No. 3, pp. 145-170 (in Ukrainian. English summary).