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Journal of the Korea Society for Industrial and Applied Mathematics
Journal Basic Information
pISSN :
1226-9433
eISSN :
1229-0645
Journal DOI :
10.12941/jksiam
Frequency :
Others
Publisher:
The Korean Society for Industrial and Applied Mathematics
Editor in Chief :
Kim Chongam
Volume & Issues
Volume 7, Issue 2 - Dec 2003
Volume 7, Issue 1 - Jun 2003
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1
A
SURFACE EXTENSION METHOD USING SEVERAL CONTROL FUNCTIONS
Kim, Hoi-Sub ; Ko, Kwan-Pyo ; Yoon, Gang-Joon ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 7, issue 2, 2003, Pages 1~11
Abstract
We suggest a method of
surface extension with the aid of well-controlled functions. The extended surface is
continuous along the old boundary. The function of the extension surface is obtained by replacing the monomials in the quadratic Taylor polynomial of the given surface-representing function by other functions subject to some boundary conditions. We present several sets of control functions. In order to illustrate our suggestion, it is shown that surfaces with a circular boundary and a square boundary can be extended using several base functions.
2
SIMULATIONS IN OPTION PRICING MODELS APPLIED TO KOSPI200
Lee, Jon-U ; Kim, Se-Ki ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 7, issue 2, 2003, Pages 13~22
Abstract
Simulations on the nonlinear partial differential equation derived from Black-Scholes equation with transaction costs are performed. These numerical experiments using finite element methods are applied to KOSPI200 in 2002 and the option prices obtained with transaction costs are closer to the real prices in market than the prices used in Korea Stock Exchange.
3
CONTROLLABILITY OF PERTURBED INTEGRODIFFERENTIAL SYSTEMS WITH PRESCRIBED CONTROLS
Balachandran, K. ; Sakthivel, K. ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 7, issue 2, 2003, Pages 23~34
Abstract
In this paper we establish a set of sufficient conditions for the controllability of perturbed integrodifferential systems with prescribed controls by using the Schaefer fixed point theorem.
4
FINITE VOLUME ELEMENT METHODS FOR NONLINEAR PARABOLIC INTEGRODIFFERENTIAL PROBLEMS
Li, Huanrong ; Li, Qian ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 7, issue 2, 2003, Pages 35~49
Abstract
In this paper, finite volume element methods for nonlinear parabolic integrodifferential problems are proposed and analyzed. The optimal error estimates in
as well as some superconvergence estimates in
are obtained. The main results in this paper perfect the theory of FVE methods.
5
ON NUMERICAL PROPERTIES OF COMPLEX SYMMETRIC HOUSEHOLDER MATRICES
Smoktunowicz, Alicja ; Grabarski, Adam ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 7, issue 2, 2003, Pages 51~64
Abstract
Analysis is given of construction and stability of complex symmetric analogues of Householder matrices, with applications to the eigenproblem for such matrices. We investigate numerical properties of the deflation of complex symmetric matrices by using complex symmetric Householder transformations. The proposed method is very similar to the well-known deflation technique for real symmetric matrices (Cf. [16], pp. 586-595). In this paper we present an error analysis of one step of the deflation of complex symmetric matrices.
6
A NUMERICAL METHOD FOR SOLVING THE NONLINEAR INTEGRAL EQUATION OF THE SECOND KIND
Salama, F.A. ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 7, issue 2, 2003, Pages 65~73
Abstract
In this work, we use a numerical method to solve the nonlinear integral equation of the second kind when the kernel of the integral equation in the logarithmic function form or in Carleman function form. The solution has a computing time requirement of
, where (2N +1) is the number of discretization points used. Also, the error estimate is computed.
7
MULTIGRID METHOD FOR AN ACCURATE SEMI-ANALYTIC FINITE DIFFERENCE SCHEME
Lee, Jun-S. ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 7, issue 2, 2003, Pages 75~81
Abstract
Compact schemes are shown to be effective for a class of problems including convection-diffusion equations when combined with multigrid algorithms [7, 8] and V-cycle convergence is proved[5]. We apply the multigrid algorithm for an semianalytic finite difference scheme, which is desinged to preserve high order accuracy despite of singularities.
8
GENERALIZED SYSTEMS OF RELAXED
NONLINEAR VARIATIONAL INEQUALITIES AND PROJECTION METHODS
Verma, Ram U. ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 7, issue 2, 2003, Pages 83~94
Abstract
Let K be a nonempty closed convex subset of a real Hilbert space H. Approximation solvability of a system of nonlinear variational inequality (SNVI) problems, based on the convergence of projection methods, is given as follows: find elements
such that
and $$<\;{\rho}T(y^*)+g(x^*)-g(y^*),\;g(x)-g(x^*)\;{\geq}\;0\;{\forall}\;g(x){\in}K\;and\;for\;{\rho}>0$$ $$<\;{\eta}T(x^*)+g(y^*)-g(x^*),\;g(x)-g(y^*)\;{\geq}\;0\;{\forall}g(x){\in}K\;and\;for\;{\eta}>0,$$ where T:
is a relaxed
and
continuous nonlinear mapping on H and g:
is any mapping on H. In recent years general variational inequalities and their algorithmic have assumed a central role in the theory of variational methods. This two-step system for nonlinear variational inequalities offers a great promise and more new challenges to the existing theory of general variational inequalities in terms of applications to problems arising from other closely related fields, such as complementarity problems, control and optimizations, and mathematical programming.
9
AN EFFICIENT IMPLEMENTATION OF BDM MIXED METHODS FOR SECOND ORDER ELLIPTIC PROBLEMS
Kim, J.H. ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 7, issue 2, 2003, Pages 95~111
Abstract
BDM mixed methods are obtained for a good approximation of velocity for flow equations. In this paper, we study an implementation issue of solving the algebraic system arising from the BDM mixed finite elements. First we discuss post-processing based on the use of Lagrange multipliers to enforce interelement continuity. Furthermore, we establish an equivalence between given mixed methods and projection finite element methods developed by Chen. Finally, we present the implementation of the first order BDM on rectangular grids and show it is as simple as solving the pressure equation.