In this paper, 2 extragradient methods for solving differential variational inequality (DVI) problems are presented, and the convergence conditions are derived. It is shown that the presented extragradient methods have weaker convergence conditions in comparison with the basic fixed-point algorithm for solving DVIs. Then the linear complementarity systems, as an important and practical special case of DVIs, are considered, and the convergence conditions of the presented extragradient methods are adapted for them. In addition, an upper bound for the Lipschitz constant of linear complementarity systems is introduced. This upper bound can be used for adjusting the parameters of the extragradient methods, to accelerate the convergence speed.Finally, 4 illustrative examples are considered to support the theoretical results. KEYWORDS differential variational inequality, extragradient method, fixed point problem, linear complementarity system, optimal control problem, variational inequalities Math Meth Appl Sci. 2017;40:7201-7217.wileyonlinelibrary.com/journal/mma
In this paper, a Jacobi collocation method is presented for solving differential variational inequalities (DVIs). Differential variational inequalities consist of a differential equation and a variational inequality. A type of Jacobi-Gauss collocation scheme with N knots is applied to the differential part of the problem whereas another type of Jacobi-Gauss collocation scheme with N + 1 knots is applied to the variational part of it. So the DVI problem turns into a variational inequality problem. Electrical circuits with nonsmooth elements like ideal diodes are an important class of physical systems, which can be modeled as DVI problems. So in the numerical experiments, 1 example with smooth solutions and 4 illustrative examples of simple electrical circuits with ideal diodes are considered. Numerical results demonstrate the effectiveness of the proposed method but slow convergence for the proposed method for some examples. The reason for slow convergence in this method is that the solutions of these DVIs are nonsmooth. KEYWORDS collocation method, differential variational inequality, variational inequality Int J Numer Model. 2019;32:e2466.wileyonlinelibrary.com/journal/jnm
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