2019
Том 71
№ 6

All Issues

Luchka A. Y.

Articles: 21
Article (Ukrainian)

Methods for the solution of boundary-value problems for weakly nonlinear integro-differential equations with parameters and restrictions

Luchka A. Y., Nesterenko O. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 5. - pp. 672-679

We establish conditions for the existence of solutions of boundary-value problems for weakly nonlinear integro-differential equations with parameters and restrictions. We also substantiate the applicability of iterative and projection-iterative methods for the solution of these problems.

Article (Ukrainian)

Iterative Method for the Solution of Linear Equations with Restrictions

Kucheruk T. A., Luchka A. Y.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 472-482

We propose a new approach to the investigation of linear equations with restrictions. For the problem considered, we establish consistency conditions and justify the application of an iterative method.

Article (Ukrainian)

Methods for the investigation of systems of differential equations with pulse influence

Luchka A. Y.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 189–194

We establish consistency conditions for a system of differential equations with pulse influence and additional conditions. The applicability of approximate methods to problems of this type is justified.

Anniversaries (Ukrainian)

Anatolii Mikhailovich Samoilenko (on his 60th birthday)

Berezansky Yu. M., Boichuk О. A., Korneichuk N. P., Korolyuk V. S., Koshlyakov V. N., Kulik V. L., Luchka A. Y., Mitropolskiy Yu. A., Pelyukh G. P., Perestyuk N. A., Skorokhod A. V., Skrypnik I. V., Tkachenko V. I., Trofimchuk S. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 3–4

Anniversaries (Ukrainian)

Bohdan Iosypovych Ptashnyk

Gorbachuk M. L., Luchka A. Y., Mitropolskiy Yu. A., Samoilenko A. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1155–1156

Anniversaries (Ukrainian)

Yurii Dmitrievich Sokolov (on his 100th birthday)

Gorbachuk M. L., Luchka A. Y., Mitropolskiy Yu. A., Samoilenko A. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1443-1445

Article (Ukrainian)

Methods for the solution of equations with restrictions and the Sokolov projection-iterative method

Luchka A. Y.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1501-1509

We establish consistency conditions for equations with additional restrictions in a Hilbert space, suggest and justify iterative methods for the construction of approximate solutions, and describe the relationship between these methods and the Sokolov projection-iterative method.

Article (Ukrainian)

Solution of volterra integral equations of the second kind with small nonlinearities by a spline-iteration method

Luchka A. Y., Mamatov T. D.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 433–437

We consider and justify a spline-iteration method for solving Volterra integral equations of the second kind with small nonlinearities.

Article (Ukrainian)

Variational-iterative method for integral equations

Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 12. - pp. 1626–1635

Article (Ukrainian)

Variational-iterative method for nonlinear equations

Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1328–1338

Article (Ukrainian)

Yurii Dmitrievich Sokolov (on his ninetieth birthday)

Luchka A. Y., Mitropolskiy Yu. A., Shevelo V. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 534–538

Article (Ukrainian)

Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 534–538

Article (Ukrainian)

Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 6. - pp. 797–799

Article (Ukrainian)

Rate of convergence of the projection-iterative method for integral equations

Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1981. - 33, № 2. - pp. 190–198

Article (Ukrainian)

A projection-iterative method for solving integral equations based on interpolation splines

Luchka A. Y., Tukalevskaya N. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 6. - pp. 683–691

Article (Ukrainian)

On the rate of convergence of some projection methods for linear operator equations

Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1971. - 23, № 3. - pp. 307–317

Article (Ukrainian)

Convergence and stability of the Ritz method

Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1968. - 20, № 5. - pp. 713–717

Anniversaries (Russian)

Yurij Dmitrievich Sokolov (on his sixtieth birthday)

Kurpel N. S., Luchka A. Y., Mitropolskiy Yu. A., Shevelo V. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1966. - 18, № 4. - pp. 94-101

Brief Communications (Russian)

On a non-standard iterative method of the approximate solution of linear operator equations

Kurpel N. S., Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 389-396

Article (Russian)

Approximate solution of linear operator eqmtions in a Banach space by Yu. D. Sokolov's Method

Luchka A. Y.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1961. - 13, № 1. - pp. 39-52

Yu. D. Sokolov's method was applied to obtain approximate solutions (16) of the linear operator equation (2) in a Banach space. The sufficient condition $L_k < 1$ (29) for the convergence of the process is derived; estimates of the error (41), (42) and (44) are given; and the efficacy of Yu. D. Sokolov's method is illustrated by examples.

Article (Russian)

Approximate Solution of Fredholm Integral Equations by the Method of Averaged Functional Corrections

Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 32-46