Publication Date:
2012-07-10
Description:
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 )± j h ( t ) to determine the existence region of the exact solution for each . Moreover, we have . Numerical examples of bridge collapse, earthquake-induced structural pounding and circuit simulation are given to illustrate the efficiency of the error bound.
Print ISSN:
0272-4979
Electronic ISSN:
1464-3642
Topics:
Mathematics
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