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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.
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].
SPECTRAL ANALYSIS OF THE MGSS PRECONDITIONER FOR SINGULAR SADDLE POINT PROBLEMS
RAHIMIAN, MARYAM,SALKUYEH, DAVOD KHOJASTEH The Korean Society for Computational and Applied M 2020 Journal of applied mathematics & informatics Vol.38 No.1
Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1, 1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.
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.
PHENOMENA AND PROPERTIES OF ROOTS OF BERNOULLI-FIBONACCI POLYNOMIALS
CHEON SEOUNG RYOO The Korean Society for Computational and Applied M 2024 Journal of applied and pure mathematics Vol.6 No.1
In this paper, we investigate the distribution of the zeros of the Bernoulli-Fibonacci polynomials by using computer.
DATA MINING AND PREDICTION OF SAI TYPE MATRIX PRECONDITIONER
Kim, Sang-Bae,Xu, Shuting,Zhang, Jun The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.1
The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods are considered the preferred methods. Selecting a suitable preconditioner with appropriate parameters for a specific sparse linear system presents a challenging task for many application scientists and engineers who have little knowledge of preconditioned iterative methods. The prediction of ILU type preconditioners was considered in [27] where support vector machine(SVM), as a data mining technique, is used to classify large sparse linear systems and predict best preconditioners. In this paper, we apply the data mining approach to the sparse approximate inverse(SAI) type preconditioners to find some parameters with which the preconditioned Krylov subspace method on the linear systems shows best performance.
JUNG YOOG KANG The Korean Society for Computational and Applied M 2023 Journal of applied and pure mathematics Vol.5 No.5
In this paper, we construct a fully modified q-poly-Euler numbers and polynomials of the second type and give some properties. Finally, we investigate the zeros of the fully modified q-poly-Euler numbers and polynomials of the second type by using computer.