Integral bvp for singularly perturbed system of differential equations
Dauylbayev M.K. Konisbayeva K.T. Tortbay N.R.
25 June 2021al-Farabi Kazakh State National University
International Journal of Mathematics and Physics
2021#12Issue 125 - 33 pp.
Thc article presents a two-point integral BVP for singularly perturbed systems of linear ordinary differential equations. The integral BVP for singularly perturbed systems of ordinary differential equations previously has not been considered. The paper shows the influence of nonlocal boundary conditions on the asymptotic of the solution of the regarded BVP and the significant effect of integral terms in the definition of the limiting BVP. An explicit constructire formula for the solution of this BVP using initial and boundary functions of the homogeneous perturbed equation is obtained. A theorem on asymptotic estimates of the solution and its deriratires is giren. It is established that the solution of the integral BVP at the point t = 0 is infinitely large as μ → 0.From here, it follows that the solution of the considered boundary ralue problem has an initial jump of zero order. It is found that the solution of the original integral BVP is not close to the solution of the usual limiting unperturbed BVP. A changed limiting BVP is obtained. The presence of integrals in the boundary conditions leads to the fact that the limiting BVP is determined by the changed boundary conditions. This follows from the presence of the jump and its order. A theorem on the close between the solutions of the original perturbed and changed limiting problems is giren.
Asymptotic , Asymptotic estimate , BVP , Initial jumps , Singularly perturbation , Small parameter
Text of the article Перейти на текст статьи
Al-Farabi Kazakh National University, Kazakhstaninstitute of InformationandComputattonal Technologies, Almaty, Kazakhstan
Al-Farabi Kazakh National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026