Current Issue : October - December Volume : 2013 Issue Number : 4 Articles : 7 Articles
The perturbed systems of sines, which appear when solving some partial differential equations by the Fourier method, are\r\nconsidered in this paper. Basis properties of these systems in weighted Sobolev spaces of functions are studied....
This investigation deals with the Falkner-Skan flow of a Maxwell fluid in the presence of nonuniform applied magnetic field with\r\nheat transfer. Governing problems of flow and heat transfer are solved analytically by employing the homotopy analysis method\r\n(HAM). Effects of the involved parameters, namely, theDeborah number,Hartman number, and the Prandtl number, are examined\r\ncarefully. A comparative study is made with the known numerical solution in a limiting sense and an excellent agreement is noted....
Implementation of interval arithmetic in complex problems has been hampered by the tedious programming exercise needed to\r\ndevelop a particular implementation. In order to improve productivity, the use of interval mathematics is demonstrated using\r\nthe computing platform INTLAB that allows for the development of interval-arithmetic-based programs more efficiently than\r\nwith previous interval-arithmetic libraries. An interval-Newton Generalized-Bisection (IN/GB) method is developed in this\r\nplatform and applied to determine the solutions of selected nonlinear problems. Cases 1 and 2 demonstrate the effectiveness of\r\nthe implementation applied to traditional polynomial problems. Case 3 demonstrates the robustness of the implementation in\r\nthe case of multiple specific volume solutions. Case 4 exemplifies the robustness and effectiveness of the implementation in the\r\ndetermination ofmultiple critical points for a mixture of methane and hydrogen sulfide.The examples demonstrate the effectiveness\r\nof the method by finding all existing roots with mathematical certainty....
In many recent works, many authors have demonstrated the usefulness of fractional\r\ncalculus in the derivation of particular solutions of a significantly large number of\r\nlinear ordinary and partial differential equations of the second and higher orders. The\r\nmain objective of the present paper is to show how this simple fractional calculus\r\nmethod to the solutions of some families of fractional differential equations would\r\nlead naturally to several interesting consequences, which include (for example) a\r\ngeneralization of the classical Frobenius method. The methodology presented here is\r\nbased chiefly upon some general theorems on (explicit) particular solutions of some\r\nfamilies of fractional differential equations with the Laplace transform and the\r\nexpansion coefficients of binomial series....
We established (????/??)-expansion method for (2+1)-dimensional nonlinear evolution equations.This method was used to construct\ntravelling wave solutions of (2+1)-dimensional nonlinear evolution equations. (2+1)-Dimensional breaking soliton equation, (2+1)-\ndimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation, and (2+1)-dimensional Bogoyavlenskii�s Breaking soliton equation\nare chosen to illustrate the effectiveness of the method....
In this paper, we consider a dual Internet congestion control algorithm applied to a\r\nnonstandard finite-difference scheme, which responds to congestion signals from the\r\nnetwork. By choosing delay as a bifurcation parameter, the local asymptotic stability\r\nof the positive equilibrium and the existence of Neimark-Sacker bifurcations are\r\nanalyzed. Then the explicit algorithm for determining the direction of Neimark-Sacker\r\nbifurcations and the stability of invariant closed curves are derived. In addition, we\r\ngive specific examples to illustrate the phenomenon that coincides with our\r\ntheoretical results....
Performances of the conventional finite elements are closely related to the mesh quality. Once distorted elements are used, the\r\naccuracy of the numerical results may be very poor, or even the calculations have to stop due to various numerical problems.\r\nRecently, the author and his colleagues developed two kinds of finite element methods, named hybrid stress-function (HSF) and\r\nimproved unsymmetric methods, respectively.The resulting plane element models possess excellent precision in both regular and\r\nseverely distorted meshes and even performvery well under the situations in which other elements cannot work. So, they are called\r\nshape-free finite elements since their performances are independent to element shapes. These methods may open new ways for\r\ndeveloping novel high-performance finite elements. Here, the thoughts, theories, and formulae of above shape-free finite element\r\nmethods were introduced, and the possibilities and difficulties for further developments were also discussed....
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