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Bulletin of TUIT: Management and Communication Technologies

Abstract

In this article, the interval expansion of the structure of solving basic types of boundary value problems for partial differential equations of the second order of making the basic operations that compose interval arithmetic is developed. For the differential equation (1) of the type, when constructing the interval expansion of the structure of the formula, structural formulas were used to construct with the R-function method and 4 problems were studied — the Dirichlet problem, the Neumann problem, the third type problem, the mixed boundary conditions problem. For the Dirichlet problem, the solution is an interval expansion of the structure in the form (5), where �={�� ,��̅,�̅�,�̅�̅} и [ �,�̅]is an indefinite interval function. For the Neumann problem, a solution is solved in the interval extension of the structure (10), (11), [ �1,�1̅̅̅̅], [ �2,�2̅̅̅̅] is an indefinite interval function and �1 is a differential operator of the form (9). For the problem of the third type, the solution is solved in the interval extension of the structure (16), (17), [ �1,�1̅̅̅̅], [ �2,�2̅̅̅̅] - indefinite, interval function, �1- differential operator of the form (9). For the problem, mixed boundary conditions are treated. The solution In the interval extension of the structure (22), (23), (24),[ �1,�1̅̅̅̅], [ �2,�2̅̅̅̅] is an indefinite interval function and �1is a differential operator of the form (9).

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