Algorithm for solving a class of one-dimensional variational inequalities

We consider one-dimensional variational inequalities with end constraints. An exact difference scheme and truncated difference schemes of any order of accuracy are constructed for this problem. The accuracy of the rank-m truncated scheme in the grid norm of C is O(h^2m+2). An algorithm for the implementation of the difference schemes is proposed. The algorithm reduces to two sweeps.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 24–30, 1988.