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

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... off errors into account. In particular, we compute two trajectories x h j (t) ± h j (t) to determine the existence region of the exact solution x j (t), i.e., x h . Numerical examples of bridge collapse, earthquake-induced structural pounding and circuit simulation are given to illustrate the efficiency of the error bound. Keywords: ordinary differential equations; linear variational inequalities; time-stepping method; error bounds. Here we restrict our study to the case where the subset K is a box and the mapping F is affine, that is, where l ∈ {R ∪ −∞} m and u ∈ {R ∪ ∞} m with l < u, and where M ∈ R m×m and q ∈ R m . Such a problem is called a box-constrained linear variational inequality problem or mixed linear complementarity problem (see Billups