Current Issue : April - June Volume : 2015 Issue Number : 2 Articles : 6 Articles
This paper is concerned with a local method for the solution of one-dimensional parabolic equation with nonlocal boundary\nconditions. The method uses a coordinate transformation. After the coordinate transformation, it is then possible to obtain exact\nsolutions for the resulting equations in terms of the local variables. These exact solutions are in terms of constants of integration that\nare unknown. By imposing the given boundary conditions and smoothness requirements for the solution, it is possible to furnish\na set of linearly independent conditions that can be used to solve for the constants of integration. A number of examples are used\nto study the applicability of the method. In particular, three nonlinear problems are used to show the novelty of the method....
The aim of this study is to examine some numerical tests of Pad�´e approximation for some typical functions with singularities such\nas simple pole, essential singularity, brunch cut, and natural boundary. As pointed out by Baker, it was shown that the simple pole\nand the essential singularity can be characterized by the poles of the Pad�´e approximation. However, it was not fully clear how the\nPad�´e approximation works for the functions with the branch cut or the natural boundary. In the present paper, it is shown that the\npoles and zeros of the Pad�´e approximated functions are alternately lined along the branch cut if the test function has branch cut, and\npoles are also distributed around the natural boundary for some lacunary power series and random power series which rigorously\nhave a natural boundary on the unit circle. On the other hand, Froissart doublets due to numerical errors and/or external noise\nalso appear around the unit circle in the Pad�´e approximation. It is also shown that the residue calculus for the Pad�´e approximated\nfunctions can be used to confirm the numerical accuracy of the Pad�´e approximation and quasianalyticity of the random power\nseries....
Symbolic computation techniques are used to obtain a canonical form for polynomial matrices arising from discrete 2D linear\nstate-space systems. The canonical form can be regarded as an extension of the companion form often encountered in the theory\nof 1D linear systems. Using previous results obtained by Boudellioua and Quadrat (2010) on the reduction by equivalence to Smith\nform, the exact connection between the original polynomial matrix and the reduced canonical form is set out. An example is given\nto illustrate the computational aspects involved....
The combined effect of viscous heating and convective cooling on Couette flow and heat transfer characteristics of water base\nnanofluids containing Copper Oxide (CuO) and Alumina (Al2O3) as nanoparticles is investigated. It is assumed that the nanofluid\nflows in a channel between two parallel plates with the channel�s upper plate accelerating and exchange heat with the ambient\nsurrounding following the Newton�s law of cooling, while the lower plate is stationary and maintained at a constant temperature.\nUsing appropriate similarity transformation, the governingNavier-Stokes and the energy equations are reduced to a set of nonlinear\nordinary differential equations. These equations are solved analytically by regular perturbation method with series improvement\ntechnique and numerically by an efficientRunge-Kutta-Fehlberg integration technique coupled with shooting method.Theeffects of\nthe governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop andNusselt number are presented\ngraphically, and discussed quantitatively....
We consider a class of fuzzy linear system of equations and demonstrate some of the existing challenges. Furthermore,we explain the\nefficiency of this model when the coefficientmatrix is an H-matrix. Numerical experiments are illustrated to show the applicability\nof the theoretical analysis....
Previous analyses of Laguerre�s iteration method have provided results on the behavior of this popular method when applied to the\npolynomials Pn(z) = zn ? 1, n ? N. In this paper, we summarize known analytical results and provide new results. In particular,\nwe study symmetry properties of the Laguerre iteration function and clarify the dynamics of the method. We show analytically\nand demonstrate computationally that for each n ? 5 the basin of attraction to the roots is a subset of an annulus that contains\nthe unit circle and whose Lebesgue measure shrinks to zero as n ? ?. We obtain a good estimate of the size of the bounding\nannulus. We show that the boundary of the basin of convergence exhibits fractal nature and quasi self-similarity. We also discuss\nthe connectedness of the basin for large values of n.We also numerically find some short finite cycles on the boundary of the basin\nof convergence for n = 5, ..., 8. Finally, we demonstrate that when using the floating point arithmetic and the general formulation of\nthemethod, convergence occurs even fromstarting values outside of the basin of convergence due to the loss of significance during\nthe evaluation of the iteration function....
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