This paper is concerned with the linear approximation method (i.e. the iterative method in which a sequence of vectors is generated by solving certain linearized subproblems) for solving the variational inequality. The global convergent iterative process is proposed by applying the continuation method, and the related problems are discussed. A convergent result is obtained for the approximation iteration (i.e. the iterative method in which a sequence of vectors is generated by solving certain linearized subproblems approximately).  

A third order small parameter method and its Nordsieck expression are given in this paper. It is based on Gear's method of order 2 and order 3. For moderate stiff problems this method is suitable.
In [1] we proposed a second order numerical method for stiff ODEs. The purpose of this paper is to raise the order from 2 to 3 and give its Nordsieck expression, making it automatically suit varying stepsize calculation.

This paper discusses the direct boundary element method for parabolic equations in a time-dependent interval. An optimal estimate of the error in maximum norm for the boundary element collocation scheme is given.

In this paper, a class of non-linear methods proposed in [1] is discussed. A new derivation of the methods is given. The analysis based on the new derivation shows that this class of methods is not suitable for stiff problems. The numerical tests support our argument.

An algorithm combining the MG method with two types of extrapolation is given for solving finite element equations with any initial triangulation. A high order approximation to the solution of PDEs can be obtained at the cost of order O(N) of computational work.

For the eigenvalue problem on a smooth domain we prove that the Richardson extrapolation increases the accuracy from second to third order for linear finite elements, and from fourth ro fifth order for quadratic finite elements, without modification of the scheme near the boundary.