Nedialko S. Nedialkov

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Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors survey(More)
The numerical solution of initial value problems (IVPs) for ODEs is one of the fundamental problems in computation. Today, there are many well-established algorithms for solving IVPs. However, traditional integration methods usually provide only approximate values for the solution. Precise error bounds are rarely available. The error estimates, which are(More)
In interval computations, the range of each intermediate result r is described by an interval r. To decrease excess interval width, we can keep some information on how r depends on the input x = (x 1 ; : : : ; x n). There are several successful methods of approximating this dependence; in these methods, the dependence is approximated by linear functions(More)
We propose the collection, standardization, and distribution of a full-featured, production quality library for reliable scientific computing with routines using interval techniques for use by the wide community of applications developers. 1 Vision – Why are we doing this? The interval/reliable computing research community has long worked to attract(More)
DAESA, Differential-Algebraic Equations Structural Analyzer, is a MATLAB tool for structural analysis of differential-algebraic equations (DAEs). It allows convenient translation of a DAE system into MATLAB and provides a small set of easy-to-use functions. DAESA can analyze systems that are fully nonlinear, high-index, and of any order. It determines(More)
Aiming at automatic verification and analysis techniques for hybrid discrete-continuous systems, we present a novel combination of enclosure methods for ordinary differential equations (ODEs) with the iSAT solver for large Boolean combinations of arithmetic constraints. Improving on our previous work, the contribution of this paper lies in combining iSAT(More)
Verified methods for the integration of initial value problems (IVPs) for in ordinary differential equations (ODEs) aim at computing guaranteed error bounds for the flow of an ODE while maintaining a low level of overestimation. This paper is concerned with one of the sources of over-estimation: a matrix-vector product describing a parallelepiped in phase(More)