Usmanov, K. I. Nazarova, K. Zh. Yerkisheva, Zh. S.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this paper, we consider a boundary value problems for a systems of loaded integro-differential equations with an involutory transformation. The parameterization method is applied to the boundary value problem for a system with continuous kernel. By using the properties of involutory transformation, the problem is transformed to a boundar...

Assanova, A. T. Sabalakhova, A. P. Toleukhanova, Z. M.
Published in
Lobachevskii Journal of Mathematics

AbstractThe family of boundary value problems for a system of integro-differential equations of mixed type is considered. First, considered problem is reduced to the family of boundary value problems for the Fredholm integro-differential equations with an unknown function and the integral relation. Further, based on the introduction of an additiona...

Minglibayeva, B. B. Assanova, A. T.
Published in
Lobachevskii Journal of Mathematics

AbstractThe nonlinear two-point boundary value problem with parameter for systems of ordinary differential equations is investigated by the parametrization method. The method consists in partition of the interval apart, the introduction of additional parameters and reducing the original problem to the equivalent multi-point boundary value problem w...

Temesheva, S. M. Dzhumabaev, D. S. Kabdrakhova, S. S.
Published in
Lobachevskii Journal of Mathematics

AbstractA two-parameter family of algorithms for finding an approximate solution to a linear two-point boundary value problem for a system of ordinary differential equations is offered. The convergence conditions for the algorithms are obtained. The necessary and sufficient coefficient conditions for the well-posedness of considered problem are est...

Dzhumabaev, D. S.
Published in
Computational Mathematics and Mathematical Physics

family of algorithms for solving a linear two-point boundary value problem is constructed in terms of the data of the integrodifferential equation and the boundary condition involved. The convergence conditions for the algorithms are established, and necessary and sufficient conditions for the well-posedness of the problem are found.

Dzhumabaev, D. S.
Published in
Computational Mathematics and Mathematical Physics

A method for solving the linear boundary value problem for an integro-differential equation is proposed that is based on interval partition and the introduction of additional parameters. Necessary and sufficient conditions for the solvability of the problem are obtained.

Dzhumabaev, D. S. Temesheva, S. M.
Published in
Computational Mathematics and Mathematical Physics

A sharper version of the local Hadamard theorem on the solvability of nonlinear equations is proved. Additional parameters are introduced, and a two-parameter family of algorithms for solving nonlinear two-point boundary value problems is proposed. Conditions for the convergence of these algorithms are given in terms of the initial data. Using the ...