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- Nedialko Stoyanov Nedialkov, Nedialko Stoyanov, Luis Seco
- 1999

Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated (also called interval) 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… (More)

- Nedialko S. Nedialkov, Kenneth R. Jackson, George F. Corliss
- Applied Mathematics and Computation
- 1999

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)

- Nedialko S. Nedialkov, Kenneth R. Jackson, John D. Pryce
- Reliable Computing
- 2001

This paper is one of a series underpinning the authors' DAETS code for solving DAE initial value problems by Taylor series expansion. First, building on the second author's structural analysis of DAEs (BIT 41 (2001) 364–394), it describes and justifies the method used in DAETS to compute Taylor coefficients (TCs) using automatic differentiation. The DAE may… (More)

- Nedialko S. Nedialkov, Kenneth R. Ja kson
- 1999

- Markus Neher, Kenneth R. Jackson, Nedialko S. Nedialkov
- SIAM J. Numerical Analysis
- 2007

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)

- Mahmoud Khademi, Nedialko S. Nedialkov
- 2015 IEEE 14th International Conference on…
- 2015

We propose a probabilistic graphical model (PGM) for prognosis and diagnosis of breast cancer. PGMs are suitable for building predictive models in medical applications, as they are powerful tools for making decisions under uncertainty from big data with missing attributes and noisy evidence. Previous work relied mostly on clinical data to create a… (More)

- Nedialko S. Nedialkov, Kenneth R. Jackson
- Reliable Computing
- 1999

We investigate solution techniques for numerical constraint satisfaction problems and validated numerical set integration methods for computing reachable sets of nonlinear hybrid dynamical systems in presence of uncertainty. To use interval simulation tools with higher dimensional hybrid systems, while assuming large domains for either initial continuous… (More)

The authors have developed a Taylor series method for solving numerically an initial-value problem differential algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit, see BIT 45:561–592, 2005 and BIT 41:364-394, 2001. Numerical results have shown this method to be efficient and very accurate, and particularly suitable… (More)