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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)

- N. S. Nedialkov
- 2002

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 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)

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)

We overview the current state of interval methods and software for computing bounds on solutions in initial value problems (IVPs) for ordinary differential equations (ODEs). We introduce the VNODE-LP solver for IVP ODEs, a successor of the author's VNODE package. VNODE-LP is implemented entirely using literate programming. A major goal of the VNODE-LP work… (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)

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)