MATHEMATICAL SCIENCES
Year:2012 | Volume:6 | Issue:-|Papers Count:6

Purpose: In this paper, a detailed analysis of an important nonlinear model system, the two dimensional generalized Kuramoto-Sivashinsky (2D gKS) equation, is presented by group analysis.Methods: The basic Lie symmetry method is applied in order to determine the general symmetry group of our analyzed nonlinear model.Results: The symmetry group of the equation and some results related to the algebraic structure of the Lie algebra of symmetries are obtained. Also, a complete classification of the subalgebras of the symmetry algebra is resulted.Conclusions: It is proved that the Lie algebra of symmetries admits no three dimensional subalgebra. Mainly, all the group invariant solutions and the similarity reduced equations associated to the infinitesimal symmetries are obtained.

Purpose: In this paper, we shall investigate the numerical solution of two-dimensional Fredholm integral equations (2D-FIEs).Methods: In this work, we apply two-dimensional Haar wavelets, to solve linear two dimensional Fredholm integral equations (2D-FIEs). Using 2D Haar wavelets and their properties, 2D-FIEs of the second kind reduce to a system of algebraic equations.Results: The numerical examples illustrate the efficiency and accuracy of the method.Conclusions: In comparison with other bases (for example, polynomial bases), one of the advantages of this method is, although the involved matrices have a large dimension, they contain a large percentage of zero entries, which keeps computational effort within reasonable limits.

Our purpose in this paper is researching about characteristics of convergent in probability and almost surely convergent in Serstnev space. We prove that if two sequences of random variables are convergent in probability (almost surely), then, sum, product and scalar product of them are also convergent in probability (almost surely). Meanwhile, we will prove that each continuous function of every sequence convergent in probability sequence is convergent in probability too. Finally, we represent that for independent random variables, every almost surely convergent sequence is convergent in probability. In this paper, we conclude results in Serstnev space are similar to probability space.

Purpose: The purpose of this paper is to extend a generalized convergence method, namely, statistical convergence to sequences of fuzzy numbers of multiplicity greater than two.Methods: We use analytic method to obtain our results.Results: Certain theorems on statistical convergence of real double sequences obtained by Savas et al. and Moricz are also extended to multiple sequences of fuzzy numbers. Finally, we define Cesaro summable and strongly p-Cesaro summable multiple sequences of fuzzy numbers and obtained their relations with statistical convergence.Conclusions: Although, we prove our results only for triple sequences, but all these results remain true for d-multiple sequences as well.

In this paper, numerical integration rules based on block-pulse functions and Chebyshev wavelet are proposed to find approximate values of definite integrals. Errors of these numerical integrations are given. These numerical integrations are compared by sinc functions numerical integration method. Some numerical examples are provided to illustrate the accuracy of proposed rules and comparison between them. The main advantage of proposed numerical integration methods are their efficiency and simple applicability.

Purpose: This paper investigates an analytical approximate solution of a fourth-order differential equation with nonlinear boundary conditions modeling beams on elastic foundations using iterative reproducing kernel method.Methods: The solution obtained using the method takes the form of a convergent series with easily computable components. However, the reproducing kernel method can not be used directly to solve the problems since there is no method of obtaining a reproducing kernel satisfying nonlinear boundary conditions. The aim of this paper is to fill this gap.Results: Several illustrative examples are given to demonstrate the effectiveness of the present method.Conclusions: Results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for the beam equation with third-order nonlinear boundary conditions.