Applied Mathematics

The purpose of this paper is to present a numerical analysis of an unsteady three dimensional MHD flow of dusty fluid past an infinite inclined porous plate in presence of Soret effect, Dufour effect, radiation effect and Hall effect with variable temperature and concentration embedded in porous medium. At time t^'>0 the plate moves with constant velocity u_0 and at the same time, the plate temperature and concentration levels near the plate decreased exponentially with time t'. The governing boundary layer equations of flow problem are transformed into non linear partial differential equations using non dimensional quantities and solved numerically by Crank-Nicolson finite difference method. The obtained results for velocity profiles along x^' direction and z' direction, temperature profile and concentration profile are discussed through graphs and physical significance of quantities skin friction, Nusselt number, Sherwood number also discussed through tables. It is found that there are slightly change in velocity profile in x'-axis but measure change in z'-axis.

A numerical study of viscoelastic buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power-law according to and respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then non-dimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter and semi-vertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the non-porous study by Hossain and Paul [9] and are found to be in excellent agreement. The local skin friction, Nusselt number and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes and hybrid solar energy systems.

In this paper, the parameters governing the arm model of a robot has been studied through a numerical technique “fourth order non-linear extended RK method based on Centroidal Mean (RKCeM)”. The exact solutions of the system of second order equations representing the arm model of a Robot have been compared with the corresponding discrete solutions (approximate solutions) at different time and also the absolute error between the exact and discrete solutions has been determined.

In this work, we introduced the novel computational algorithm for solving linear and nonlinear system of partial differential equation by using the projected differential transform method. Several illustrative examples are demonstrated to show the efficiency of the projected differential transform for solving initial value problems .All numerical results compared with those obtained by another analytic and numerical method; such as Adomain decomposition, variational iteration and spline method are found to be the same.

A new integral transform similar to Laplace and Sumudu transforms is introduced, to explain the use of Tarig transform in differential equations, an example of first and second order linear differential equations are presented. In this work we show that the applicability of this interesting new transform its very efficiency to solving differential equations with constant coefficients.

Complete Bipartite graph is the most important graph in design theory. There are several ways of constructing Complete Bipartite graph. In this paper we suggested an algorithm which can be used to construct Complete Bipartite graph using the Hadamard matrices. If the Order of Hadamard matrix is n then resultant Complete Bipartite graph is K_(n,n) where n is even . The proposed method was tested manually for n=2,4. Higher order Complete Bipartite graph were constructed using java program.

In this paper I try to prove some relation about convergence of infinite series and infinite sequence. And also try to prove that if and are any two positive term convergent series then are also convergent series. And also try to give some examples which gives the support to the comparison test.

The aim of this paper is to introduce the stronger forms of nano gb-continuous functions namely, nano gb-irresolute function, strongly nano gb-continuous functions and perfectly nano gb-continuous functions and to establish the relationship between them. Also some of their properties of those functions are derived.

A numerical method for solving fuzzy Volterra-Fredholm integral equation of the second kind will is introduced. We convert a nonlinear fuzzy Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. We use Adomian Decomposition Method (ADM) to find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy Volterra-Fredholm integral equation. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.

The main objective of this paper is to establish two summation formulae based on half argument involving Contiguous Relation. The results derived in this paper are of general character.