MATHEMATICAL SCIENCES
Year:2011 | Volume:5 | Issue:4|Papers Count:8

This paper presents an efficient method for solving free vibration problems for an Euler-Bernoulli beam under various supporting conditions. The method is based on the implementation of the sixth-order compact finite difference method (CFDM) for discretizing the governing differential equation to obtain the natural frequencies of beam corresponding to two commonly used boundary conditions namely simply supported-simply supported and clamped-free. A very good agreement is found between the natural frequencies obtained using the sixth-order compact finite difference scheme and exact natural frequencies, which confirms the validity of the present sixth-order discretization.

In this paper, we prove the generalized Hyers-Ulam stability of a cubic functional equation in non-Archimedean spaces.

In this paper, we introduce a new concept named generalized (j-k)-B contraction and prove a theorem about existence and uniqueness of fixed point in generalized (j-k)-B contraction on complete Menger space.

We develop a numerical method for solution the Hammerstein integral equations by using the Gauss-Legendre quadrature. The presented method yield a nonlinear system of 10´10 only, which is an advantage of our method in comparison with the existing methods. This method has been tested to six test problems of various kinds to show the applicability and accuracy of presented approach.

In this paper hybrid functions which consist of Block-Pulse functions plus Leg-endre polynomials are developed to approximate the solution of the linear Volterra integral equations system that arises in the elastodynamic problems. Properties of these hybrid functions are first presented, the operational matrix of integration and the product operational matrix are utilized to reduce the computation of Volterra integral equations system to some algebraic equations. Finally numerical results which we compared them with some existed method are given to showing the profit and efficiency of the proposed method.

We introduce the notion of approximately injectivity for Banach modules. For a locally compact group G, we study the approximately injectivity of Banach L1 (G)- modules.

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In this paper, we introduce a new technique in semi-analytic method for solving non-linear differential equations. At first, a non-linear differential equation will be converted to a linear differential equation (or some of them) by using homotopy method. Then, for finding parameter a in the linear differential equation we use Galerkin method, which is easier and less computations in comparison with similar methods, such as [5, 7]. Then, we will solve linear differential equation by using analytic method where it's evident that analytic method is better than the vibrational iteration method in [1, 3]. Also in [7] perturbation techniques are depend on small parameter but the above mentioned method is not depend on small parameter. The obtained results are shown the high accuracy.