2019
Том 71
№ 11

# 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

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

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

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)

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

Anniversaries (Ukrainian)

### Bohdan Iosypovych Ptashnyk

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

Anniversaries (Ukrainian)

### Yurii Dmitrievich Sokolov (on his 100th birthday)

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

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.

Brief Communications (Russian)

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

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

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

Article (Ukrainian)

### Variational-iterative method for nonlinear equations

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

Article (Ukrainian)

### Yurii Dmitrievich Sokolov (on his ninetieth birthday)

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

Article (Ukrainian)

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

Article (Ukrainian)

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

Article (Ukrainian)

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

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

Article (Ukrainian)

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

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

Article (Ukrainian)

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

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

Article (Ukrainian)

### Convergence and stability of the Ritz method

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

Anniversaries (Russian)

### Yurij Dmitrievich Sokolov (on his sixtieth birthday)

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

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

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

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