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Numerical solution of boundary value problems modelled by differential or integral equations is reduced to solving linear system of equations. Even in the systems of equations without intervals, the solution does not have to be unique, e.g., in the case of a singular (or at least ill-conditioned) matrix. Such problems are even more inconvenient in the interval linear systems of equations. In this paper, the various methods of solving such systems are tested. These systems have been generated during the numerical solution of boundary value problems modelled by Navier-Lamé equations.

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The paper presents an unambiguous modelling of imprecisely defined shapes of closed curves using classical and directed interval arithmetic. The authors focus on the development of an effective strategy of modelling interval smooth closed curves (which enforce C 2 continuity in points at which adjacent interval segments join) using interval cubic Bézier segments. For this purpose, algebraic relationships between Bézier and de Boor control points, formerly known for precisely defined curves, are generalized. We obtain interval control points that define interval closed curves. Additionally, the reliability of such way of modelling of closed curves is examined. We directly apply classical and directed interval arithmetic to mentioned relationships and try to solve obtained interval systems of algebraic equations. However, we obtain ambiguous solutions. Therefore, we propose our new strategy of modification of directed interval arithmetic to obtain reliable and unambiguous shapes of interval closed curves.

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