Modeling the shape of boundary using NURBS curves directly in modified boundary integral equations for Laplace's equation

The main purpose of this study is the modification of the parametric integral equations systems (PIES) method, to include the NURBS curves into its mathematical formulas. We want to create an opportunity for defining the boundary shape using NURBS curves without the classical discretization process. We present an inclusion of the NURBS curves into PIES, and its application in process of modeling and solving the boundary value problems, on Laplace's equation example. The correctness and accuracy of such modeling is confirmed by the examples. Obtained solutions are compared with these obtained using linear segments and B-spline curves. Additionally, we verify the correctness of modeling and modifying the shape using analytical solutions. The NURBS curves significantly expand the possibilities and increase the accuracy of the boundary shape modeling which is an important aspect of the numerical solving of boundary value problems.