Verification of interval PIES solutions on examples of uncertainly defined boundary value problems modeled by Laplace's equation

摘要

In this paper we propose new methods of interpretation and verification of interval solutions obtained using interval parametric integral equations systems (interval PIES). These strategies concern the examples with the analytical solutions as well as more sophisticated examples. To obtain errors of precisely defined solutions (for comparison with interval ones), we base on well known methods of errors calculation. All of considered boundary value problems examples are described by Laplace's equation. For modeling the uncertainty of boundary value problems we propose the modified directed interval arithmetic, which was previously applied in mentioned interval PIES method.