Concept of modeling uncertainly defined shape of the boundary in two-dimensional boundary value problems and verification of its reliability

The paper presents the concept of modeling uncertainly defined shape of the boundary in two-dimensional boundary value problems described by Laplace equation. The authors propose generalization of parametric integral equations system (PIES) in modeling and solving the problems. Previously, PIES was successfully applied to model precisely defined problems. Pseudo-spectral method and modified interval arithmetic are used to define the boundary of the problem and to obtain numerical solution of generalized PIES. We examine direct application of interval Bézier curves in PIES and then we propose our new concept of modeling of the shape of the boundary to improve the reliability of solutions.