Computational error bounds for a differential linear variational inequality

Xiaojun Chen, Zhengyu Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

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 xh(t) delivered by the time-stepping method, which takes all discretization and roundoff errors into account. In particular, we compute two trajectories xjh(t)±εjh(t) to determine the existence region of the exact solution xj(t),ie.,xjh(t) ≤ xj(t) ≤ xjh(t) + ∈jh(t) for each j ∈ {1,⋯,n}. Moreover, we have ∈jh(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.
Original languageEnglish
Pages (from-to)957-982
Number of pages26
JournalIMA Journal of Numerical Analysis
Volume32
Issue number3
DOIs
Publication statusPublished - 1 Jul 2012

Keywords

  • error bounds
  • linear variational inequalities
  • ordinary differential equations
  • time-stepping method

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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