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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Botoroeva M. N.
,
Budnikova O. S.
,
Solovarova L. S.
SAMPLING BOUNDARY CONDITIONS FOR SECOND ORDER DIFFERENTIAL-ALGEBRAIC EQUATIONS // BSU bulletin. Mathematics, Informatics. - 2019. №3. . - С. 32-41.
Title:
SAMPLING BOUNDARY CONDITIONS FOR SECOND ORDER DIFFERENTIAL-ALGEBRAIC EQUATIONS
Financing:
Ботороева М. Н. поддержана грантом РФФИ, № 18-51-54001_Вьет_а, и Мини- стерством образования и науки РФ, проект 1.5049.2017/БЧ; Будникова О. С. под- держана грантом РФФИ, № 18-51-54001_Вьет_а; Соловарова Л. С. поддержана грантом РФФИ, № 18-29-10019 мк.
Codes:
DOI: 10.18101/2304-5728-2019-3-32-41UDK: 519.624.2
Annotation:
The article considers systems of second-order linear ordinary differential equations with an identically degenerated square matrix preceding the second derivative (sec- ond order differential-algebraic equations). Such problem statements often arise in applications. We have noted the difficulties in qualitative study and development of numerical methods for solving the equations under consideration. It is assumed that boundary conditions are given and their number is less than the doubled dimension of the initial system. We have defined a class of second order differential-algebraic equations, and using the known results of projection theory proposed an algorithm for sampling the missing boundary conditions. The method developed is illustrated by a simple example. At the conclusion of the article we have paid attention to the further research of this algorithm.
Keywords:
boundary value problem; boundary conditions; differential-algebraic equations; ordinary second order degenerate differential equations; tridiagonal ma- trix algorithm; initial boundary value problem; algebraic-differential equations; numerical methods; second order differential equations; three-point approximation.
List of references:
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