Solving the two-dimensional laplace equation by the method of boundary integral equations

On the basis of the boundary integral equation method high accuracy numerical algorithm for solving Laplace's equation on a plane with regions with sectionally smooth bound is constructed. The method accuracy is estimated and expansion over degrees of discrediting step for approximate solutions is established. This expansion allows one to applicate the Richardson type extrapolation. Efficiency of extrapolation on mesh sequence is illustrated by numerical example, the accuracy obtained of approximate solutions and finite-difference method solutions are compared