Current Issue : April - June Volume : 2018 Issue Number : 2 Articles : 5 Articles
Any polyhedron accommodates a type of potential theoretic skeleton called a\nmother body. The study of such mother bodies was originally from Mathematical\nPhysics, initiated by Zidarov [1] and developed by Bj�¶rn Gustafson\nand Makoto Sakai [2]. In this paper, we attempt to apply the brilliant idea of\nmother body to Electrostatics to compute the potentials of electric fields....
Recently many research works have been conducted and published regarding\nfractional order differential equations. There are several approaches available\nfor numerical approximations of the solution of fractional order diffusion equations.\nSpectral collocation method based on Lagrange�s basis polynomials to\napproximate numerical solutions of one-dimensional (1D) space fractional\ndiffusion equations are introduced in this research paper. The proposed form\nof approximate solution satisfies non-zero Dirichlet�s boundary conditions on\nboth boundaries. Collocation scheme produce a system of first order Ordinary\nDifferential Equations (ODE) from the fractional diffusion equation. We applied\nthis method with four different sets of collocation points to compare\ntheir performance....
This paper is concerned with the initial-boundary value problem of scalar\nconservation laws with weak discontinuous flux, whose initial data are a function\nwith two pieces of constant and whose boundary data are a constant\nfunction. Under the condition that the flux function has a finite number of\nweak discontinuous points, by using the structure of weak entropy solution of\nthe corresponding initial value problem and the boundary entropy condition\ndeveloped by Bardos-Leroux-Nedelec, we give a construction method to the\nglobal weak entropy solution for this initial-boundary value problem, and by\ninvestigating the interaction of elementary waves and the boundary, we clarify\nthe geometric structure and the behavior of boundary for the weak entropy\nsolution....
The study suggests asymptotic behavior of the solution to a new class of difference equations: . where a, bi, Ã?± and Ã?² are positive real numbers for i = 0, 1, Ã?· Ã?· Ã?· , k , and the initial conditions ÃË?-j, ÃË?-j+1, Ã?· Ã?· Ã?·, ÃË?0 are randomly positive real numbers where j = 2k + 1. Accordingly, we consider the stability, boundedness and periodicity of the solutions of this recursive sequence. Indeed, we give some interesting counter examples in order to verify our strong results....
In this paper, we develop a method for evaluating one dimensional singular\nintegrals (weakly, strongly, and hyper-singular) that converge in the sense of\nCauchy principal value and Hadamard finite part integrals. A proof of convergence\nof this method is also provided...
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