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ROJA, J. CHRISTY,TAMILSELVAN, A. The Korean Society for Computational and Applied M 2017 Journal of applied mathematics & informatics Vol.35 No.3
In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.
OBLIQUE PROJECTIONS AND SHIFT-INVARIANT SPACES
Park, Sang-Don,Kang, Chul Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.5
We give an elementary proof of one of the main results in [H.O. Kim, R.Y. Kim, J.K. Lim, The infimum cosine angle between two finitely generated shift-invariant spaces and its applications, Appl. Comput. Har-mon. Anal. 19 (2005) 253-281] concerning the existence of an oblique projection onto a finitely generated shift-invariant space along the orthogonal complement of another finitely generated shift-invariant space under the assumption that the generators generate Riesz bases.
CONSTRUCTION OF CARTESIAN AUTHENTICATION CODES OVER UNTITRAY GEOMETRY
Xu, Wenyan,Gao, You The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
A construction of Cartesian authentication codes over unitary geometry is presented and its size parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities of success for different types of attacks are also computed.
SPECTRAL METHODS AND HERMITE INTERPOLATION ON ARBITRARY GRIDS
Jung, H.S.,Ha, Y.S. The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.3
In this paper, spectral scheme based on Hermite interpolation for solving partial differential equations is presented. The idea of this Hermite spectral method comes from the spectral method on arbitrary grids of Carpenter and Gottlieb [J. Comput. Phys. 129(1996) 74-86] using the Lagrange interpolation.
REMARKS ON THE WIENER POLARITY INDEX OF SOME GRAPH OPERATIONS
Faghani, Morteza,Ashrafi, Ali Reza,Ori, Ottorino The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.3
The Wiener polarity index$W_p(G)$ of a graph G of order $n$ is the number of unordered pairs of vertices $u$ and $v$ of G such that the distance $d_G(u,v)$ between $u$ and $v$ is 3. In this paper the Wiener polarity index of some graph operations are computed. As an application of our results, the Wiener polarity index of a polybuckyball fullerene and $C_4$ nanotubes and nanotori are computed.
Gu, Guanghui,Su, Yongfu The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.1
The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].
REPRODUCING KERNEL METHOD FOR SOLVING TENTH-ORDER BOUNDARY VALUE PROBLEMS
Geng, Fazhan,Cui, Minggen The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.3
In this paper, the tenth-order linear boundary value problems are solved using reproducing kernel method. The algorithm developed approximates the solutions, and their higher-order derivatives, of differential equations and it avoids the complexity provided by other numerical approaches. First a new reproducing kernel space is constructed to solve this class of tenth-order linear boundary value problems; then the approximate solutions of such problems are given in the form of series using the present method. Three examples compared with those considered by Siddiqi, Twizell and Akram [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345-362; S.S.Siddiqi, G.Akram, Solutions of tenth-order boundary value problems using eleventh degree spline, Applied Mathematics and Computation 185 (1)(2007) 115-127] show that the method developed in this paper is more efficient.
Jun, Young-Bae,Lee, Kyoung-Ja,Ozturk, Mehmet Ali The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
Molodtsov [D. Molodtsov, Soft set theory First results, Comput. Math. Appl. 37 (1999) 19-31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCC-algebras. The notion of (trivial, whole) soft BCC-algebras and soft BCC-subalgebras are introduced, and several examples are provided. Relations between a fuzzy subalgebra and a soft BCC-algebra are given, and the characterization of soft BCC-algebras is established.