Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

In a finite neighborhood of each singular point on the boundary (the vertices of the reentrant angle, the points of discontinuity of the given boundary functions, and the points of change of the type of boundary conditions), a special integral representation of the solution is approximated by the quadrature formulas of regtangles, which converges exponentially. On the outside of the chosing neighborhoods, the Laplace equation and the boundary conditions are approximated by the finite difference method. The equations obtained in this combined method are connected by constructing the high accurate matching operator. The error of the approximate solution in uniform metric and its any order derivatives in the choosing neighborhoods is estimated. The possibility of solving the system of algebraic equations obtained in this method by Schwarz alternating procedure is justified. Numerical results are presented to conform the high accuracy of the proposed method.

Note. Abstracts are published in author's edition

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