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International Journal of Applied Mathematics and Computation

The effect of imposed time-periodic boundary temperature of small amplitude on electroconvection under AC electric field in dielectric couple stress liquids is investigated by making a linear stability analysis. A regular perturbation method is used to arrive at an expression for the correction Rayleigh number that throws light on the possibility of sub-critical motions. The Venezian approach is adopted for obtaining eigen value of the problem. Three cases of oscillating temperature field are examined: (a) symmetric, so that the wall temperatures are modulated in phase, (b) asymmetric, corresponding to out-of phase modulation and (c) only the lower wall is modulated.  It is shown that the system is most stable when the boundary temperatures are modulated out-of-phase. 2014/08/22 - 05:50

The purpose of this article is to present non-polynomial spline approximations using non-uniform mesh for the numerical treatment of singular boundary value problems. The numerical method is compact and exhibit homogeneous fourth order of convergence. The resulting nonlinear difference schemes are solved by alternating group explicit parallel algorithm. The utility of new schemes are illustrated by Burger’s equation, Duffing equation and Thomas Fermi model. Computational order of convergence and maximum absolute errors are given to demonstrate the efficiency of the non-uniform mesh approach. 2014/08/22 - 05:50

In this paper, optimal control problem described by discrete-time linear Volterrasystem is studied by the conventional minimization method of Lagrange multipliers. 2014/08/22 - 05:50

In this paper, we investigate the first integral method for solvingthe solutions of nonlinear Generalized Zakharov Equations. This ideacan obtain some exact solutions of this equations based on the theoryof Commutative algebra. 2014/08/22 - 05:50

This paper introduces a new Monte Carlo algorithm for solving integro-differential equations. Finally, comparing the results of this algorithm with numerical Gauss-Legendre method is considered. 2014/08/22 - 05:50

By using the direct algebra method, the traveling wave solutions forthe Hamiltonian amplitude equation and the higher-order nonlinearSchr\"{o}dinger equation are constructed. The obtained resultsinclude complex exponential function solutions, complex travelingsolitary wave solutions, complex periodic wave solutions. The powerof this manageable method is confirmed.\\The Hamiltonian amplitude equation is an equation which governscertain instabilities of modulated wave trains, with the additionalterm $-\epsilon u_{xt}$ overcoming the ill-posedness of the unstablenonlinear Schr\"{o}dinger equation. It is a Hamiltonian analogue ofthe Kuramoto-Sivashinski equation which arises in dissipativesystems and is apparently not integrable.\\ 2014/08/22 - 05:50

We investigate the numerical-complete solution of the generalized higher order difference equation to find the value of m-series to the product of polynomials and polynomial factorials in the field of finite difference methods. We also provide suitable examples, verified by Matlab programming, to illustrate the m-series. 2014/03/21 - 19:41

By means of the two distinct methods, the direct algebraic method and the cosine method, we successfully performed an analytic study on the (2+1)-dimensional cubic nonlinear  Schr\"{o}dinger equation. 2014/03/21 - 19:41

The combine effect of the hall current, rotation, radiation and chemical reaction on MHD oscillatory free convective, dusty, viscoelastic, incompressible and electrically conducting fluid in an infinite porous vertical channel has been analysed. A uniform injection/ suction velocity is applied at the plates and uniform magnetic field of uniform strength is applied in the direction normal to the plane of the plates. The entire system rotatesabout the axis normal to the planes of the plates with uniform angular velocity. The solution of the equations governing the flow are obtained for fluid velocity, dust particle velocity, temperature and concentration profile. The effect of the various parameters entering in the governing equations on flow are evaluated numerically and discussed with the help of graphs and tables. 2014/03/21 - 19:41

Values of Tthe parametes are determined for which there exist positive solutions of the system of four-point nonlinear boundary value problems satisfying four-point boundary value problems. A Guo-Krasnosel'skii xed point- theorem is applied. 2014/03/21 - 19:41

The fractional Riccati equation with  Riemann-Liouville derivatives has been successively used to find the explicit solutions of the space-time of nonlinear fractional partial differential equations.Three  models of special interest with fractional space-time derivative of order $\alpha$,$0<\alpha<1$ are considered. The three models are tested to illustrate the pertinent feature of the proposed algorithm.This approach can also be applied to other nonlinear fractional differential equations arising in mathematical physics. 2014/03/21 - 19:41

A problem of propagation of strong plane and converging shock wave is studied in unsteady, Darcy-type porous media. Nonstandard analysis is used to derive the jump conditions for both plane and converging shock waves. It is also assumed that the shock thickness occurs at innitesimal interval andjump functions in low parameters are smooth across this interval. The distribution of low parameters across the shock wave are expressed in terms of Heaviside functions and Dirac Delta measures. Numerical computations have been performed to study the eect of porosity of the medium on the distribution of the ow parameters. 2014/03/01 - 17:56

This paper provides a Green element  method (GEM) numerical  analysis of the effects of  a uniform transverse magnetic field on fluid flow. The Green element method is a robust numerical scheme that evolved essentially from the singular integral  theory of the boundary element method (BEM) with the unique variety of numerically implementing the theory  by  the finite element procedure. One of the advantages inherent in this approach is that the coefficient matrix from the discrete  equations of the assembled element equations is banded and amenable to numerical  solution. For the purposes of this study,   the fluid is incompressible, and electrically conducting, and  flows between two parallel plates, one of which is moving with a uniform speed  while the other is stationary. The depth of the channel is taken to be much smaller than the width and the channel is considered to be  very long in the horizontal direction. As a result,  the flow is  assumed to be fully developed and  driven by a pressure gradient in a uniform magnetic field. Numerical solutions obtained with GEM closely match analytical results. In order to validate the physics and numerics of the problem formulation,  comprehensive  parametric studies are carried out to show the effects on flow  and electromagnetic fields of Hartmann number, pressure gradient, current distributions, and temperature . 2014/03/01 - 17:56

The effect of radiation and thermal stratification on the flow of an elastico-viscous fluid past an infinite vertical plate is presented. The constitutive equations of Walter’s liquid B/ are used. Solutions for velocity and temperature fields are obtained by  Laplace transform technique for unit Prandtl number. Numerical computations for velocity, temperatures are made for different values of the physical parameters and presented in graphs. It is observed that in presence of thermal stratification and radiation both velocity and temperature reaches steady state at smaller time. Observations are also made on other physical phenomenon like skin friction, Nusselt number. 2014/03/01 - 17:56

In this paper, we will introduce the homotopy perturbation method(HPM) and the reduced differential transform method (RDTM) forsolving (1+1)-dimensional nonlinear Boussinesq equation. Theanalytical solution of the equation have been obtained in terms ofconvergent series with easily computable components. The obtainedresults show that the proposed methods are very powerful andconvenient mathematical tool for nonlinear evolution equations inscience and engineering. 2014/03/01 - 17:56

In this paper, the first integral method is used to construct exacttraveling wave solutions of $(2+1)-$ dimensional dispersive longwave equation. The first integral method is an efficient method for obtaining exact solutions some of nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. 2014/03/01 - 17:56

A single server general bulk service finite source loss model has been studied. For this model the system steady state probabilities and waiting time distributions are obtained. Some performance measures are also calculated. Particular model is deduced and some numerical examples are also given. 2014/03/01 - 17:56

In this paper, we obtain the numerical solution of the generalfractional partial differential equations. To this end, weintroduce an efficient new basis based on the generalizedfractional-order Bernstein functions. A general formulation forthe fractional Bernstein operational matrix of fractionalintegral operator and derivatives operator for the first time isobtained. In this approach, a truncated fractional Bernsteinseries together with the fractional Bernstein operational matrixare used to reduce the such problems to those of solving a systemof algebraic equations thus greatly simplifying the problem.Illustrative examples are included to demonstrate the validityand applicability of the presented technique. Presented resultsshow that the method will improve the solutions of fractionalpartial differential equations. 2013/08/10 - 18:56

This paper presents a computational technique for solving singularly perturbed boundary value problems with the boundary layer at one end. This technique is a non-iterative on small deviating argument which converts the original second order boundary value problem to the first order differential equation with the deviating argument. We use the trapezoidal method on the first order differential equation; tridiagonal scheme is obtained and is solved efficiently. Numerical examples show the validity of the present method. 2013/08/10 - 18:56

In this paper, a problem on reflection and transmission of plane waves atan imperfect interface between two dissimilar monoclinic elastic half-spaces isstudied. The boundary conditions at imperfect interface are satisfied by appropriateparticular solutions in the half-spaces to obtain a non-homogeneoussystem of four equations in amplitude ratios of reflected and transmittedwaves. The amplitude ratios of reflected and transmitted waves are computedand shown graphically for different kinds of boundaries. 2013/08/10 - 18:56

In this note we use the Nehari manifold and fibering maps to show existence of a solution for a nonlinear \emph{p}-biharmonic equation in a bounded smooth domain in $\mathbb R^N$, when $2p<N<\frac{2pq}{q-p}$. 2013/08/10 - 18:56

In this paper, the modified extended tanh method is used to construct new exact traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili equation. The modified extended tanh method is one of most direct and effective algebraic method for obtaining exact solutions of nonlinear partial differential equations. The method can be applied to nonintegrable equations as well as to integrable ones. 2012/03/03 - 05:59

A mathematical solution to Einstein's field equations with a perfect fluid source, with variable gravitational constant $G$ and Cosmological constant $\Lambda$ for FRW space-time in higher dimensions is obtained and case study has also been done where the values of $\rho(t), G(t), \Lambda(t), q(t),$ and $d_{H}(t)$ has been obtained and their nature is also analyzed. 2012/03/03 - 05:59

The distributed current in the straight cylindrical antenna can be obtained by solving the Hallen equation with certain unknown constants. In this paper the Hallen equation is reduced to a Cauchy singular integral equation (CSIE). Quadrature method is then applied to the CSIE to obtain a linear system of equations. This approach enables to resolve the unknown constants with the condition that the current vanishes at the ends. This alternative approach is now well posed. A couple of examples are worked out and distributed current is computed. 2012/03/03 - 05:59

Directable automata, known also as synchronizable, cofinal and reset automata, are a significant type of automata with very interesting algebraic properties and important applications in various branches of Computer Science. The central concept that we introduce and discuss in this paper is the concept of \pi-directable automata as a concomitant specialization concept of the directable automata and generalization of the concept definite automata. Are introduced and a new class of automata, such as trapp-directable automata, the local trap \pi-directable automata, uniformly locally trap p-directable automata, finite \pi-directable automata. 2012/03/03 - 05:59

The proof of convergence of the series solution to a class of nonlinear two-dimensional Hammerstein integral equation (NTHIE), including the necessary and su¢ cient conditions that guarantee a unique solution, is introduced. Adomian Decomposition Method (ADM) and Homotopy Analysis Method (HAM) are used to solve the NTHIE. It was found that, when using the traditional Adomian polynomials (4), ADM and HAM are exactly the same. But, when using the proposed accelerated Adomian polynomials formula (5), ADM converges faster than HAM. The proposed accelerated Adomian polynomials formula is used directly to prove the convergence of the series solution. Convergence approach is reliable enough to estimate the maximum absolute truncated error. 2012/03/03 - 05:59

Existence of both compressive and rarefactive solitons is established in weakly relativistic but magnetized plasma with cold ions and ion-beams in presence of electron inertia. It is observed that rarefactive (compressive) solitons exist for smaller (higher) difference of electron and ion initial streaming speeds for different ion to ion-beam mass ratio and wave speed. Interestingly, the amplitude of the rarefactive solitons is seen to increase with the increase of the difference of initial streaming speeds to certain limit before turning out to be compressive after that limit. 2012/03/03 - 05:59

In this paper a study of uniformly convergent method proposed by Il’in –Allen-South well scheme was made. A condition was contemplated for uniform convergence in the specified domain. This developed scheme is uniformly convergent for any choice of the diffusion parameter. The search provides a first- order uniformly convergent method with discrete maximum norm. It was observed that the error increases as step size h gets smaller for mid range values of perturbation parameter. Then an analysis carried out by [16] was employed to check the validity of solution with respect to physical aspect and it was in agreement with the analytical solution. The uniformly convergent method gives better results than the finite difference methods. The computed and plotted solutions of this method are in good – agreement with the exact solution. 2012/03/03 - 05:59

A steady laminar two-dimensional boundary layer flow of a viscous incompressible radiating fluid over an exponentially stretching sheet, in the presence of transverse magnetic field is studied. The non-linear partial differential equations describing the problem under consideration, are transformed into a system of ordinary differential equations using similarity transformations. The resultant system is solved by applying Runge-Kutta fourth order method along with shooting technique. The flow phenomenon has been characterized by the thermo physical parameters such as magnetic parameter (M), radiation parameter (R) and Eckert number (E). The effects of these parameters on the fluid velocity, temperature, wall skin friction coefficient and the heat transfer coefficient have been computed and the results are presented graphically and discussed quantitatively. 2012/03/03 - 05:59

In this paper, we introduce a new intelligent combination method based on Multilayer Perceptron Neural Network (MLP‐NN) and Hybrid Genetic Algorithm (HGA) for automotive price forecasting. The combination of MLPNN and HGA lead us to accelerate convergence to the optimal weights and improve the forecasting performance. In this structure, the Levenberg‐ Marquardt (LM) algorithm is employed for training of the network, and the hybridization of Genetic Algorithm (GA) with some local search optimization techniques such as steepest descent (SD) method and quasi‐Newton methods with DFP and BFGS formula is used to perform HGA. We apply our new hybrid model to forecast the automotive prices in Iran Khodro Company which is the biggest automotive manufacturing in IRAN. Simulation results show the enough reduction in the processing iterations and forecasting error which is mean square error. The results are well promising compared to the cases when we apply MLP‐NN or hybridization of MLP‐NN and GA, individually. 2011/08/20 - 13:14

In this paper numerical solution of Fokker-Planckequations by means of the Chebyshev spectral collocation method is considered. Firstly, properties of the Chebyshev spectral collocation method required for our subsequent development are given and utilized to r duce the computation of different kinds of Fokker-Planck equations to some system of ordinary differential equations. Secondly, we use fourth-order Runge-Kutta formula for the numerical solution of the system of ordinary differential equations. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method. 2011/08/20 - 13:14

The direct solution of general second order ordinary differential equation is considered in this paper. The method is based on the collocation and interpolation of the power series approximate solution to generate a continuous linear multistep method. We modified the existing block method in order to accommodate the general nth order ordinary differential equation. The modified block is adopted to generate the independent solution at the grid points. This method was found to be efficient when tested on second order ordinary differential equation 2011/08/20 - 13:14

The direct algebraic method is an effective algebraic method for obtaining the exact solution of nonlinear partial differentialequations. The method can be applied to nonintegrable equations as well as to integrable ones. In this paper,we look for the exact solution of the $(3+1)$-dimensional Kadomtsev-Petviashvili (KP) equation. 2011/08/20 - 13:14

In this paper, the generalized (G′/G)-expansion method is used for construct an innovative explicit traveling wave solutions involving parameters of the generalized combined KdVand mKdV equation u_{t}+a(t)u_{x}+u u_{x}+u² u_{x}-u_{xxx}=0, for any arbitray function a(t), there is no any method before, gave any exact solution for this equation. 2011/08/20 - 13:14

In this paper, necessary and sufficient condition is established for controllability of discrete time linear Volterra systems. Local controllability result for a semi-linear discrete Volterra system is also proved. Numerical examples are provided to illustrate our results. 2011/08/20 - 13:14

Consider a single server retrial queueing system with non-pre-emptive priority service and variable service rates in which two types of customers arrive in a Poisson process with arrival rate λ1 for low priority customers and λ2 for high priority customers.We assume that the regular service times follow an exponential distribution with parameters μ1 and μ2 for both types of customers respectively. The retrial is introduced for low priority customers only.The concept of variable service rate (accelerated service) is introduced in this paper and it follows the exponential distribution with parameter µ3. The access from orbit to the service facility follows the classical retrial policy and the high priority customers will be governed by the non-pre-emptive priority service.This model is solved by using Matrix geometric Technique.Numerical  study  have been done for   Analysis of  Mean number of low priority customers in the orbit (Mnco),Mean number of high priority customers in the queue, Truncation level (O_cut),Probability of server free and Probabilities  of server busy with low and high priority customers for various values of λ1 ,  λ2 , μ1 , µ2 , µ3 ,  σ and k  in elaborate manner and also various particular cases of  this model have been discussed. 2011/08/20 - 13:14