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Тезисы докладов

Численное решение дифференциальных и интегральных уравнений

In numerical analysis, a substantial “arsenal” of approximate methods for solution of boundary value problems with elliptic operators has been accumulated. These methods, as a rule, solve a problem based on a system of algebraic equations with matrices of very high order. An alternative method with respect to the difference and the variational-difference algorithms is offered. It is intended for solving a boundary value problem with the second order elliptic operator in a two-dimensional domain combined of rectangles. Coefficients of a differential operator are assumed to be piecewise constant, i.e. are constant inside each rectangle. In a general case the classical solution in the given statement does not exist, and therefore an approximate solution of the problem is realized in a generalized version. The proposed method is based on the splitting of a differential operator, and it is aimed at using a specific system of the basis functions ensuring approximation of the solution by means of their small number. The final objective is the following: to attain an increasingly small dimension of a algebraic system of equations, rapid convergence rate of iterative process as well as essentially decreased computer memory.

Примечание. Тезисы докладов публикуются в авторской редакции

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