Point-Interval Technique of an Estimation of a Sensitivity Numerical Solution of the Elliptic Equations

K. F. Ivanova , e-mail: klara.i2010@yandex.ru

In work the estimation of an error of a unknown vector received at modeling of physical processes and technical constructions by Poisson's equations is offered. As a rule, the solution of the partial differential equations is obtained after the discretization by systems of linear algebraic equations (SLAE) with rarefied matrixes. The analysis of sensitivity of system is based on an aprioristic estimation of its reaction to influence of the entrance data expressed in intervals, corresponding to errors of boundary conditions and source function. The offered technique of an estimation of an error of the solution can help to reveal nodes of a real construction or a power field which are the most vulnerable at occurrence of extreme deviations. The received estimations guarantee reliability of calculations necessary for prevention of dangerous situations at practical realization of models of thermal and electromagnetic processes, stationary problems of building mechanics and for many other physical and technical problems.

Keywords: Poisson's equations, modeling, approximation, intervals, sensitivity, an estimation of an error, extreme deviations.

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