Interval Arithmetics in Modeling and Solving Uncertainly Defined Boundary Value Problems of Elasticity
Eugeniusz Zieniuk, Marta Kapturczak, Krzysztof Szerszeń · 2019
In this paper, the idea of modeling and solving boundary value problems, with the uncertainly defined boundary shape, is presented. For this purpose, the modification of the method of parametric integral equations system (PIES) is proposed. During tests, based on examples of exactly defined problems, its advantages over alternative methods have been repeatedly emphasized. That is why, it was decided to modify this method for solving uncertainly defined problems. For modeling uncertainty of the boundary shape and for numerical calculations the modification of directed interval arithmetic was proposed. Obtained numerical interval solutions will be compared with interval analytical solutions. Such solutions can be obtained using classical and directed interval arithmetic, as well as the modification of directed interval arithmetic.