Abstract
The paper presents a modification of the traditional Boundary Integral Equation Method (BIEM) for two-dimensional potential type boundary-value problems with a linear-segments boundary. This modification consists in describing the linear segments of the boundary by parametric linear functions. As a result of these analytical modifications of the BIEM, a new parametric integral equation system (PIES) with the kernels of the integral equations including the geometry of the boundary, was obtained. The PIES is not defined on the boundary as in the BIEM, but on a line and its solution does not require a segment discretization since it reduces only to an approximation of the boundary functions. To solve this PIES, the pseudosprectral method is employed and the obtained results are compared with the results received on the basis of the BIEM.
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