Band 14, Heft 5

This paper applies differential transform – Pade technique for treating non-linear singular boundary value problems arising in various physical problems of science and engineering. Comparisons are made between the results of the proposed method, and the exact solutions. The results show that the proposed method is an attractive method for solving non-linear singular boundary value problems.

In this paper, we utilize the first integral method with symbolic computation to constructing periodic and solitary wave solutions of complex nonlinear evolution equations. With the aid of Maple, new exact solutions of two nonlinear evolution equations in physics, namely, generalized Zakharov equations (GZ) and higher-order nonlinear Schrodinger equation (HONLS) describing propagation of ultrashort pulses in nonlinear optical fibers are obtained.

Recently some generalizations of Sylvester type tridiagonal matrices have been considered with their spectra. We introduce a new kind generalization of Sylvester type tridiagonal matrix by considering its main diagonal entries. Then we compute its spectra and determinant.

Wavelet function generates significant interest from both theoretical and applied research given in the last ten years. In the present paper, the Daubechies family of wavelets will be considered due to their useful properties, since the contribution of compactly supported wavelet by Daubechies and multi resolution analysis based on Fast Fourier Transform (FWT) algorithm by Beylkin, wavelet based solution of ordinary and partial differential equations gained momentum in attractive way. Advantages of Wavelet-Galerkin method over finite difference or element method have led to tremendous application in science and engineering. In this paper, the Daubechies families of wavelets have been applied to solve differential equations. Solution obtained with the Daubechies' 6 Wavelet filter coefficients has been compared with exact solution. The good agreement of the result with the exact solution proves the accuracy and efficiency of Wavelet-Galerkin method.

This paper presents an approach to shape/topology optimization of continuous structures. The proposed approach combines the design element technique and the level set function in order to obtain an efficient topology parameterization of the domain under consideration. The shape and the level set function are both parameterized by the control points and corresponding blending functions of the design elements. For the sake of generality, nonlinear finite elements are employed, which have to be adapted adequately in order to be able to describe full material, void, and any intermediate state. In this way the design element technique has not yet been used for topology optimization, partially because it requires that the domain geometry and finite element mesh have to be defined by utilizing control-point-based design elements. In spite of this drawback, the proposed approach offers several attractive benefits. Namely, in contrast to other level set methods, the proposed approach does not make any use of the Hamilton-Jacobi differential equation. Consequently, the boundary evolution stage of the process need not to be treated separately, but is integrated with the strain/stress analysis stage into a rather conventional optimization scheme. Furthermore, the proposed approach allows for any type of finite elements (linear/nonlinear) to be implemented into the procedure if adjusted adequately. The formulation of the optimization problem is also completely arbitrary. The properties of the proposed approach are illustrated by several numerical examples.

A stagnation point flow of a viscoelastic Walters' B fluid over a surface lubricated with a power-law non-Newtonian fluid is considered in this paper. It is assumed that the lubricant is spread over the sheet making a thin layer of variable thickness. We are interested in a similarity solution of the problem which in the present case exists only for the power-law index n  = 1/2. For the other values of the power-law index the non-similar solutions are also presented in the present paper. A slip flow boundary condition is deduced for a viscoelastic fluid at the fluid-fluid interface which is then imposed on the surface due to reason that the lubrication layer is thin. This new slip boundary condition is different from the conventional slip boundary condition for viscoelastic fluids considered in the literature. The numerical solution of the governing nonlinear ordinary differential equation subject to a nonlinear slip boundary condition is obtained by a hybrid method that combines the features of the finite difference and shooting methods. The profiles of velocity under the influence of slip and viscoelastic fluid parameters are illustrated. Moreover, the behavior of the missing condition f ″(0) under the influence of these parameters is also presented. The results for the no-slip and full slip flows can be recovered as limiting cases when λ  → ∞ and λ  → 0 respectively.

Due to the health impacts caused by exposures to air pollutants in urban areas, monitoring and forecasting of air quality parameters have become popular as an important topic in atmospheric and environmental research today. The knowledge on the dynamics and complexity of air pollutants behaviour has made artificial intelligence and statistical learning models as a useful tool for a more accurate pollutant concentration prediction. The aim of this study is to build a regression model of daily air quality prediction by using support vector machine (SVM) technique in Gijón urban area (Northern Spain) at local scale. To accomplish the objective, the observed data of nitrogen oxides, carbon monoxide, sulphur dioxide, ozone and dust for years 2006 to 2008 are used to create a highly nonlinear model of the air quality in the city based on SVM techniques. One objective of this model was to make a preliminary estimate of the dependence between primary and secondary pollutants in Gijón urban area at local scale. A second aim was to determine the factors with the greatest bearing on air quality in order to propose health and lifestyle improvements. This support vector regression model captures the main insight of statistical learning theory to obtain a good prediction of the dependence among the main pollutants in Gijón urban area since it shows a good agreement between the observed and predicted values of pollutants using statistical estimators as correlation coefficients, mean errors and root mean squared errors. Finally, conclusions of this study are exposed.

Reaction-diffusion equations are ubiquitous as models of pattern formation in chemistry and biology. In this paper, the invariant subspace method is used to investigate exact solutions and the corresponding patterns in a reaction-diffusion system. Several forms of the exact solutions of the one-dimensional reaction-diffusion system are presented, including complexions. Furthermore, we show several patterns the two-dimensional reaction-diffusion system, involving stripes, spots and transitions between them. Additionally, we discuss the relations between patterns and exact solutions.

This paper focuses on the nonlinear Klein-Gordon equation with dual power law nonlinearity. The traveling wave hypothesis reveals an implicit solution in terms of Gauss' hypergeometric functions. The bifurcation analysis is subsequently carried out that gives an additional set of solutions. The phase portraits of the solutions are also given.