In this work the collocation METHOD based on quartic B-spline is developed and applied to two-POINT BOUNDARY value problem in ordinary differential equations. The error analysis and convergence of presented METHOD is discussed. The METHOD illustrated by two test examples which verify that the presented METHOD is applicable and considerable accurate.

We use cubic spline functions to develop a numerical METHOD for the solution of second-order linear two-POINT BOUNDARY value problems. The resulting linear system of equations has been solved using a tri-diagonal solver. Convergence of the METHOD is shown through standard convergence analysis. Numerical examples are given to show the applicability and efficiency of our METHOD. Also we compared our METHOD with finite difference, finite element, B-spline and finite volume METHODs which applied to the two-POINT BOUNDARY value problems.

Purpose: In this paper, we shall present an algorithm for solving more general singular second-order multi-POINT BOUNDARY value problems.METHODs: The algorithm is based on the quasilinearization technique and the reproducing kernel METHOD for linear multi-POINT BOUNDARY value problems.Results: Three numerical examples are given to demonstrate the efficiency of the present METHOD.Conclusions: Obtained results show that the present METHOD is quite efficient.

Let C be a nonempty closed convex subset of a real Hilbert space H. Let {Sn} and {Tn} be sequences of nonexpansive self-mappings of C, where one of them is a strongly nonexpansive sequence. K. Aoyama and Y. Kimura introduced the iteration process xn+1=bnxn+(1-bn) Sn (anu+(1-an) Tnxn) for finding the common fixed POINT of {Sn} and {Tn}, where uÎC is an arbitrarily (but fixed) element in C, x0ÎC arbitrarily, {an} and {bn} are sequences in [0; 1]. But in the case where uÏC, the iterative scheme above becomes invalid because xn may not belong to C. To overcome this weakness, a new iterative scheme based on the thought of BOUNDARY POINT METHOD is proposed and the strong convergence theorem is proved. As a special case, we can find the minimum-norm common fixed POINT of {Sn} and {Tn} whether 0ÎC or 0ÏC.

A three POINT variable mesh finite difference METHOD of third order, have been derived to solve the singular two-POINT BOUNDARY value problems. The METHOD reduces to a METHOD of order four for the uniform mesh case and may be considered as a modification of the well known Numerov"s METHOD. The METHODs are self starting and are exact for y=1/x. The convergence of the fourth order METHOD has also been discussed. The various measures of error for solution of two problems, using the METHODs and the fourth order METHOD in [1] are listed. The numerical results are also compared with five well known classical METHODs to show the self starting and accuracy of the present METHODs. Subject Classifications: AMS 64L10, CR: G1.7

In this research, SALCHOW algorithm has been developed to solve linear programming problems. In each step SLACHOW moves towards the constrained gradient of the objective function, so that it always remains within the feasible region. This type of generating sequence of feasible solutions on the BOUNDARY of the feasible region differs from the behavior of the simplex. Simplex moves on the corners of the feasible region. On the other hand, SALCHOW is also different from interior POINT METHODs; because interior POINT METHODs generate solutions that are not on the corner POINTs or even borders of feasible region. SALCHOW assigns a set of coefficients to some active constraints for appending to objective function and updating constrained gradient of objective function. Finally at the optimal POINT, the Lagrange coefficients of the active constraints are found. Computational results are generated by using a set of randomly generated instance problems and a few standard ones from OR-Library. These results show the superiority of SALCHOW over the simplex in these small instances. In other words, the mean time of solving an instance with SALCHOW is a function of the number of decision variables in contrast with Simplex. Runtime of simplex in the average is a function of the number of constraints. The computational errors caused by round off errors in developed code in MATLAB exhibits that our developed code for SALCHOW suffers from cumulative errors; and it obstructs the possibility of judging the definite superiority of SALCHOW over the simplex in solving small instance problems.

In this paper, we are concerned with positive solutions for higher order m{POINT nonlinear fractional BOUNDARY value problems with integral BOUNDARY conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m{POINT nonlinear fractional BOUNDARY value problems with integral BOUNDARY conditions by using some results from the theory of  xed POINT index, Avery{Henderson  xed POINT theorem and the Legget{Williams  xed POINT theorem, respectively.

One of the most important topic that consider in recent years by researcher is absolute value equation (AVE). The absolute value equation seems to be a useful tool in optimization since it subsumes the linear complementarity problem and thus also linear programming and convex quadratic programming. This paper introduce a new METHOD for solving absolute value equation. To do this, we transform absolute value equation to linear system and then demonstrate efficient augmented Lagrangian METHOD to solve the linear system. Also this paper is considered a class of two-POINT BOUNDARY value problems and introduced a new METHOD to solve them. In this paper is shown that this class of problems is equivalent to absolute value equation. To illustrate the feasibility and effectiveness our METHOD we generate random problems and solve them also solve a class of two-POINT BOUNDARY value problems. In section numerical results, we consider the efficiency of the proposed METHOD. Computational results show that convergence to high accuracy often occurs in short time.

In this paper, a Chebyshev finite difference METHOD has been proposed in order to solve nonlinear two-POINT BOUNDARY value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This METHOD can be regarded as a non-uniform finite difference scheme. The METHOD is computationally attractive and applications are demonstrated through an illustrative example. Also a comparison is made with existing results.