Journal of Applied & Computational Mathematics

Abstract Based on the quadratic extrapolation method and its generalization, this paper presents an accelerated two-level multigrid method for speeding up the numerical computation of the stationary probability vector of an irreducible Markov chain. It shows how to combine these vector extrapolation methods with the two-level multigrid method on the coarse level in detail. Numerical results on two Markov chain problems are provided to illustrate the effectiveness of our proposed method in terms of reducing the iteration counts and computing time.

The use of intelligent networks is one of the newest technologies in the electricity industry that has been considered in recent years. Rapid advancement in technology and growing daily consumption are among the main factors that cause the generation and formation of these networks and its entrance to electrical distribution systems. Considering the importance of intelligent networks, this paper introduces intelligent networks and reviews the benefits of using them, and after describing the components of these networks and its standards, some implemented samples in some countries is presented, and finally the results of a practical implementation will be reviewed.

In this paper, we propose an algorithm to obtain approximate solutions of Fractional Differential-Algebraic Equations with Caputo-type derivatives. The method, Iterative Decomposition Method presents solutions as rapidly convergent infinite series of easily computable terms. Numerical examples are considered to highlight the significant features of the IDM, as well as illustrate the efficiency and accuracy of the method, when compared with known methods.

This paper presents a location-allocation hub covering considering capacity constraints for multiple hubs and allocates non-hub nodes including the manufacturer and the customer. The model is an integer linear programming minimizing the transfer costs and optimizes the allocation requests from the manufacturer to the customer passing through one or two hubs. It also simultaneously minimize the cost allocation requests and optimize the use of any existing network hub and the use of any existing network hub due to restrictions on the transfer or collect applications to hub. The model optimization is fulfilled using Lingo 9.0 software, and a discussion is comprehensibly illustrating the aspects of the proposed model.

The algorithm proposed in this paper belongs to the methodological category of unidimensional search by elimination, and may be used, therefore, in the optimization of discontinuous functions. This new method is based on the dichotomous search algorithm and is, in many cases, superior to Fibonacci’s algorithm (up to the present considered the most efficient method of elimination), with the advantage of being much simpler.

This study mainly focuses on exploring the regional variation of the changing patterns of temperature and rainfall in Bangladesh. The analysis is based on the temperature and rainfall variation in Bangladesh over five regions as Dhaka, Cox’s Bazar, Rajshahi, Bogra and Sylhet. The duration of the study period was chosen as 1953-2012 for Dhaka, 1948-2012 for Cox’s Bazar, 1972-2012 for Rajshahi, 1958-2012 for Bogra and 1957-2012 for Sylhet. The findings of the non-parametric Mann-Kendal test revealed that significant increase of maximum temperature has been found in Cox’s Bazar and Sylhet, significant decrease of maximum temperature has been found in Dhaka and Bogra. Significant increase of minimum temperature has been found in Dhaka and Cox’s Bazar whereas significant decrease has been found in Rajshahi. Significant decrease of rainfall has been found in Rajshahi among the study region. The maximum temperature increased significantly by 0.021 Degree Celsius per year in Cox’s Bazar and Sylhet. In case of minimum temperature highest increase was found in Dhaka by 0.049 degree Celsius followed by Cox’s Bazar (0.038 degree Celsius per year) whereas significant decrease has been found in Rajshahi by 0.047 degree Celsius per year.

Exact solution of an incompressible fluid of second order type by causing disturbances in the liquid which is initially at rest due to bottom oscillating sinusoid ally has been obtained in this paper. The results presented are in terms of non-dimensional elastic-viscosity parameter (β) which depends on the non-Newtonian coefficient and the frequency of excitation (σ) of the external disturbance while considering the magnetic parameter (m) and porosity (k) of the medium into account. The flow parameters are found to be identical with that of Newtonian case as β →0 , m→0 and k→∞ .

Most authors of differential equations used integrating factor to solve linear first order ordinary differential equations. In this paper, we introduce undetermined functions method to solve linear first order ordinary differential equations. Moreover, we derive solution method for solving linear first order ordinary differential equations without applying exactness condition.

In this paper we prove the existence and multiplicity of solutions for p-laplacian problem with decaying cylindrical potential and critical exponent by using Palais-Smale condition and by splitting the Nehari manifold N in two disjoint subsets N+ and N-, thus considering the minimization problems on N+ and N- respectively.

An analytical solution is investigated for a fully developed free convective flow of a visco-elastic incompressible electrically conducting fluid past a vertical porous plate bounded by a porous medium in the presence of thermal diffusion, variable suction and variable permeability. A magnetic field of uniform strength is applied perpendicular to the plate and the presence of heat source is also considered. The novelty of the study is to investigate the effect of thermal diffusion on a visco-elastic fluid in the presence of time dependent variable suction. The importance is due to the applications of this kind of visco-elastic fluids in many industries. The coupled dimensionless nonlinear partial differential equations are transformed into a set of ordinary differential equations by using multiple parameter perturbation on velocity whereas simple perturbation method on temperature and concentration. With corresponds to these, the expressions for skin friction, Nusselt number and Sherwood number are derived. The numerical computations have been studied through figures and tables. The presence of thermal diffusion increases fluid velocity, whereas the influence of the magnetic field reduces it. In the case of heavier species, it is noticed that concentration increases with an increase in Soret number.

In this manuscript, we introduce Geo*Arithmetic Series. Mainly, we use theories and theorems on series to find partial sum of Geo*Arithmetic Series. Moreover, we show a Geo*Arithmetic Series is convergent (divergent) series whenever the absolute value of the common ratio of its terms is less than one (greater than one). Furthermore, we find the sum of a Geo*Arithmetic Series whenever the absolute value of the common ratio of its terms is less than one.

In this paper, we introduce higher integral of differential equations. Also, we solve some higher integral of differential equations. Moreover, we show all solutions of some higher integral of differential equations are also solutions of those differential equations.

An artificial neural network (ANN) has been trained with real-sample spectra of radioactive materials. Following the training stage ANN was applied to a subset of similar samples Results obtained with the ANN method are in good agreement with results obtained from traditional techniques, showing the high potentiality of ANN.

This paper deals with an empirical study of generalized linear model (GLM) for count data. In particular, Poisson regression model which is also known as generalized linear model for Poisson error structure has been widely used in recent years; it is also used in modeling of count and frequency data. Quasi Poisson model was employ for handling over and under dispersion which the data was found to be over dispersed and another way of handling over dispersion is negative binomial regression model. In this study, the two regression model were compare using the Akaike information criterion (AIC), the model with minimum AIC shows the best which implies the Poisson regression model.

Zeros of polynomial equations are analytically hard to be determined beyond the special cases of the quartic equations. Under some particular conditions, quintic and sextic polynomial equations may be solved iteratively. This paper presents analytical-graphical solution for accomplishing zeros of particular sextic polynomial equation of two real zeros. The concerned polynomial has been modeled geometrically as the radical problem in geodesy which is the geodetic height of a point on the terrain surface of the earth. The earth’s model to be adopted is the triaxial ellipsoidal surface. The achieved solution may be utilized as initial values for a convenient and convergent iterative process.

The objective of present problem is to investigate the effects of thermal diffusion, viscous dissipation, radiation and chemical reaction on a well-known non Newtonian fluid namely Kuvshinski fluid interaction on unsteady MHD flow over a vertical moving porous plate. The fluid is considered to be a gray, absorbing emitting but non scattering medium, and the Rosseland approximation is used to describe the radiative heat flux energy equation. The plate moves with constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. A uniform magnetic field acts perpendicular to the porous surface. The dimensionless governing equations are solved by using a simple perturbation law. The expressions for velocity, temperature and concentration are derived. With the aid of these the expressions for Skin friction, Nusselt number and Sherwood number are also derived. The effects of various material parameters on the above flow quantities are studied numerically with the help of figures and tables. It is observed that an increases in the Prandtl number results in a decreasing in temperature. An increase in Kr leads to decrease in both of concentration and velocity.

Purpose: The paper aims to find an analytic solution of an unsteady three dimensional Navier-Stokes equations of flow between two parallel disks by using von Karman type similarity transformation. Methodology: In this paper, the Homotopy Analysis Method (HAM) with the value of unknown convergence control parameter has been used to derive accurate analytic solution for an unsteady three dimensional Navier- Stokes equations of flow between two parallel disks. The possible optimal value of the convergence control parameter determined by increasing the order of HAM. Findings: The results obtained from HAM are compared with numerical results. The result shows that this method gives an analytic solution with high order of accuracy with a few iterations.

The main goals of reasonable geometric design of

unsymmetrical

vertical highway curves are the fulfillment of the two main aspects: sufficient value of the sight distance and avoidance of the sudden change in vertical acceleration, i.e. rider's comfort. Existing asymmetrical vertical highway curves consist of either one or two or even three curves takes the form of parabolic or cubic equations. In the favor of maintaining more sufficient sight distance and curve smoothness, we introduce a new single reverse and unsymmetrical vertical highway curve employing a quintic

polynomial

equation of odd powers. Equation parameters were determined exploiting the given beginning and end grades, and elevations of the points of vertical curvature and vertical tangency. The comparative study presented showed increment ranges between the values of 6.1% to 20.8% of the sight distance. The proposed curve proves smoothness particularly at the beginning of the curve, i.e. improvement of the rider’s comfort along the range of length up to 200 m and greater than 650 m along the curve. Finally, the study demonstrated the suitability of using the curve for different values of beginning and end grades which is impossible to be connected using the other existing curves. Geometric properties and relationships of the curve are presented and justified numerically.

In this manuscript, we introduce variation of parameter method for solving homogeneous linear second order ordinary differential equations with constant coefficients. Moreover, we derive general solution method to solve homogeneous linear second order ordinary differential equations with constant coefficients.

The effects of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous, incompressible and electrically conducting fluid on a moving inclined heated porous plate is analyzed. The nonlinear coupled partial differential equations are solved by perturbation technique. The influence of different pertinent parameters such as Grashof number (Gr), modified Grashof number (Gm), magnetic field parameter (M), heat source parameter (Ï•), chemical reaction parameter (γ), Schmidt number (Sc) and angle of inclination (α) on velocity, temperature and concentration distribution have been studied and analyzed with the help of graphs. An analysis of the coupled heat and mass transfer phenomena is provided in detail. We observed that velocity decreases for increasing values of the angle of inclination α. The results of the present study are compared with the results obtained by Chaudhary et al. and Dulal et al. in the absence of angle of inclination; our results appear to be in good agreement with the existing results.