Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/17670
Title: Computational error bounds for a differential linear variational inequality
Authors: Chen, X 
Wang, Z
Keywords: Error bounds
Linear variational inequalities
Ordinary differential equations
Time-stepping method
Issue Date: 2012
Source: IMA Journal of numerical analysis, 2012, v. 32, no. 3, p. 957-982 How to cite?
Journal: IMA Journal of Numerical Analysis 
Abstract: The differential linear variational inequality consists of a system of n ordinary differential equations (ODEs) and a parametric linear variational inequality as the constraint. The right-hand side function in the ODEs is not differentiable and cannot be evaluated exactly. Existing numerical methods provide only approximate solutions. In this paper we present a reliable error bound for an approximate solution x h(t) delivered by the time-stepping method, which takes all discretization and roundoff errors into account. In particular, we compute two trajectories x j h(t)±ε j h(t) to determine the existence region of the exact solution x j(t),ie.,x j h(t) ≤ x j(t) ≤ x j h(t) + ∈ j h(t) for each j ∈ {1,⋯,n}. Moreover, we have ∈ j h(t) = O(h). Numerical examples of bridge collapse, earthquake-induced structural pounding and circuit simulation are given to illustrate the efficiency of the error bound.
URI: http://hdl.handle.net/10397/17670
ISSN: 0272-4979
DOI: 10.1093/imanum/drr009
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