The problem with non-separated multipoint-integral conditions for high-order differential equations and a new general solution
Assanova A.T. Imanchiyev A.E.
2022Taylor and Francis Ltd.
Quaestiones Mathematicae
2022#45Issue 101641 - 1653 pp.
The problem with non-separated multipoint-integral conditions for high-order differential equations is considered. An interval is divided into m parts, the values of a solution at the beginning points of the subintervals are considered as additional parameters, and the high-order differential equations are reduced to the Cauchy problems on the subintervals for system of differential equations with parameters. Using the solutions to these problems, new general solutions to high-order differential equations are introduced and their properties are established. Based on the general solution, non-separated multipoint-integral conditions, and continuity conditions of a solution at the interior points of the partition, the linear system of algebraic equations with respect to parameters is composed. Algorithms of the parametrization method are constructed and their convergence is proved. Sufficient conditions for the unique solvability of considered problem are set. It is shown that the solvability of boundary value problems is equivalent to the solvability of systems composed. Methods for solving boundary value problems are proposed, which are based on the construction and solving these systems.
algorithm , high-order differential equations , Non-separated multipoint-integral conditions , problem with parameters , solvability
Text of the article Перейти на текст статьи
Institute of Mathematics and Mathematical Modeling, 125, Pushkin Str, Almaty, Kazakhstan
Zhubanov Aktobe Regional University, 34, A. Moldagulova Ave, Aktobe, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Zhubanov Aktobe Regional University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026