A new method for solving a class of mixed boundary value problems with singular coefficient

In [1], [2], [3], [4], [5], [6] and [7], it is very difficult to deal with initial boundary value conditions. In this paper, we give a new method to deal with boundary value conditions, the main contribution of this paper is to put mixed boundary value conditions into reproducing kernel Hilbert space. The numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.     

A new method for solving singular fourth-order boundary value problems with mixed boundary conditions

In [1], [2], [3], [4], [5], [6], [7] and [8], it is very difficult to get reproducing kernel space of problem (1). This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of fourth-order in the new reproducing kernel space. The numerical results are compared with both the exact solution and its n-order derived functions in the example. It is demonstrated that the new method is quite accurate and efficient for fourth-order problems.     

A method for constructing the polar cone of a polyhedral cone,with applications to linear multicriteria decision problems

The necessary and sufficient conditions for solution sets of linear multicriteria decision problems are given in the first part of this paper. In order to find the solution sets by applying the theorem describing the conditions, the constructions of the open polar cone and the semi-open polar cone of a given polyhedral cone are required.A method of construction of the polar cone, open polar cone, and semi-open polar cone is presented. For this purpose, edge vectors of the polar cone are introduced and characterized in terms of the generating vectors of a given polyhedral cone. It is shown that these polar cones are represented by the edge vectors.Numerical examples of linear multicriteria decision problems are solved to illustrate the construction of the polar cones and to explain the application of the theorem to obtain the solution sets.The author is grateful to Professor P. L. Yu for helpful comments concerning the development of Theorem 2.1.