• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Bulletin of the Society of Naval Architects of Korea
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• v.10 no.1
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• pp.27-32
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• 1973

This paper shows the method for obtaining the body flutter velocity and frequency for flight body which consists of low aspect ratio wing and body combination by assuming slender body of cylinderical shell structure. The stiffness matrix of the cylinderical shell is represented from Donnel eq. by the finite difference method, and also unsteady aerodynamic influence matrix is represented by the Doublet Lattice Method of Albano & Rodden. The flutter matrix can be obtained from those matrices.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.58 no.1
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• pp.85-89
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• 2009

We investigated the quench characteristics in accordance with increase of turns number of trigger coil and shunt resistance of matrix-type superconducting fault current limiter (SFCL) with $2{\times}3$ array. The matrix-type SFCL consists of the trigger part to apply magnetic field and the current-limiting part to limit fault current. The fault current limiting characteristics according to the increase of magnetic field and applied voltage were nearly same. This is because the application of magnetic field hasn't an affect on total impedance of the SFCL. When turns number of a reactor increased, the voltage difference between two superconducting units in the current-limiting part according was decreased. The resistance difference generated in two superconducting units was also decreased. Therefore, we confirmed that the differences of the critical behaviors between superconducting units were reduced by application of magnetic field. By this results, we could decide the optimum turns number of reactor to apply magnetic field.

• Journal of Electrical Engineering and Technology
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• v.9 no.6
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• pp.2049-2057
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• 2014

In this paper, a numerical method for analyzing coupling between high-altitude electromagnetic pulse (HEMP) as external field and a shielded twisted pair (STP) cable is proposed, which is based on an expanded chain matrix. Load responses of electromagnetic (EM) field excitation in uniform transmission line (TL) are solved by Baum-Liu-Tesche (BLT) equations in frequency domain, however, it is difficult to apply BLT equations to solve load responses of STP cable because the iteratively changing configuration of each twisted pairs are involved in cable. To avoid this problem and decrease memory and CPU time, we proposed the expanded chain matrix modeling method that is calculated using ABCD parameters, and applied multi-conductor transmission line (MTL) theory to consider the EMP coupling effectiveness of each twisted pairs. The results implemented by the proposed method are presented and compared with those obtained by the finite-difference time domain (FDTD) method as a kind of 3D full wave analysis.

• Journal of the Optical Society of Korea
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• v.6 no.3
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• pp.121-127
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• 2002

The operating principal of a ring laser gyroscope depends on the phase difference for the counter-propagating waves within a closed path. The reflecting mirrors mounted on the monoblock form the traveling waves. The manufacturing accuracy of the monoblock influences the traveling path of ray, the sensitivity of laser resonator for misalignments, and diffraction losses. A 3 $\times$ 3 ray transfer matrix was derived for optical components with centering and squaring errors in a ring resonator. The matrix can be utilized to predict the optical ray paths on the basis of the manufacturing errors of the monoblock as well as the misalignment of mirrors. Then the distance and orientation (o. slope) at the arbitrary plane inside the resonator along the ideal optical path can be calculated from the chain multiplication of the ray transfer matrix for each optical component in one round trip. We also show that the counter-propagating rays In a ring resonator with errors does not coincide in each round trip, which results in gain difference between two beams, and how these errors can be adjusted through the alignment procedure. Finally this 3 $\times$ 3 ray matrix formalism can be used to calculate the beam size and its displacement from the optical axis and the deviation at the diaphragm.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.909-931
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• 2015

This paper presents some new paranormed sequence spaces $X(r,s,t,p;{\Delta})$ where $X{\in}\{l_{\infty}(p),c(p),c_0(p),l(p)\}$ defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. Furthermore, the ${\alpha}$-, ${\beta}$-, ${\gamma}$-duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r,s,t,p;{\Delta})$ to X. Finally, it is proved that the sequence space $l(r,s,t,p;{\Delta})$ is rotund when $p_n$ > 1 for all n and has the Kadec-Klee property.

• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.48-58
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• 1999

The Characteristic Flux Difference Splitting (CFDS) scheme designed to adapt the characteristic boundary conditions at the wall and inflow/outflow boundary planes satisfies Roe's property U, although the CFDS Jacobian matrix is decomposed by a product of elaborate transformation matrices and explicit eigenvalue matrix. When the CFDS algorithm, thus a variant of Roe's scheme, is applied straightforwardly to hypersonic flows over a blunt body, the strong bow shock gradually breaks down near the stagnation point. This numerical instability is widely observed by many researchers employing flux-difference method, known in the literature as the carbuncle phenomenon. Many remedies have been proposed and resulted in partial cures. When the idea of Sanders et al. which identifies the minimum eigenvalues near the discontinuity present is applied to CFDS method, it is shown that the instability problem can be controlled successfully. A few flux splitting methods have also been tested and results are compared against the Nakamori's Mach 8 blunt body flow.

• ETRI Journal
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• v.45 no.4
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• pp.704-712
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• 2023

This paper presents a flexible finite-difference technique for analyzing the nonuniform guiding structures. Because the voltage and current variations along the nonuniform structure differ for each segment, this work considers the adaptable discretization steps. This technique increases the accuracy of the final response. Moreover, by applying the singular value decomposition and discarding the nonprincipal singular values, an optimal lower rank approximation of the discretization matrix is obtained. The computational cost of the introduced method is significantly reduced using the optimal discretization matrix. Also, the proposed method can be extended to the nonuniform waveguides. The technique is verified by analyzing several practical transmission lines and waveguides with nonuniform profiles.

• Journal of Korea Water Resources Association
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• v.42 no.4
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• pp.331-341
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• 2009

In this study, we compared the observed information matrix with the Fisher information matrix to estimate the uncertainty of maximum likelihood estimators of the generalized logistic (GL) distribution. The previous literatures recommended the use of the observed information matrix because this is convenient since this matrix is determined as the part of the parameter estimation procedure and there is little difference in accuracy between the observed information matrix and the Fisher information matrix for large sample size. The observed information matrix has been applied for the generalized logistic distribution based on the previous study without verification. For this purpose, a simulation experiment was performed to verify which matrix gave the better accuracy for the GL model. The simulation results showed that the variance-covariance of the ML parameters for the GL distribution came up with similar results to those of previous literature, but it is preferable to use of the Fisher information matrix to estimate the uncertainty of quantile of ML estimators.

• Computational Structural Engineering
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• v.10 no.1
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• pp.193-200
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• 1997

Even though there are many analysis methods of circular tanks on elastic foundation, the finite element method is widely used for that purpose. But the finite element method requires a number of memory spaces, computation time to solve large stiffness equations. In this study many the simplified methods(Analogy of Beam on Elastic Foundation, Foundation Stiffness Matrix, Finite Element Method and Transfer Matrix Method) are applied to analyze a circular tank on elastic foundation. By the given analysis methods, BEF analogy and foundation matrix method, the circular tank was transformed into the skeletonized frame structure. The frame structure was divided into several finite elements. The stiffness matrix of a finite element is related with the transfer matrix of the element. Thus, the transfer matrix of each finite element utilized the transfer matrix method to simplify the analysis of the tank. There were no significant difference in the results of two methods, the finite element method and the transfer matrix method. The transfer method applied to a circular tank on elastic foundation resulted in four simultaneous equations to solve completely.