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

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.18 no.6
• /
• pp.674-680
• /
• 2008

A new meshless method for obtaining natural frequencies of arbitrarily shaped plates with the free boundary condition is introduced in the paper. In order to improve the characteristics of convergence and accuracy of the method, a special local polar coordinates system is devised and located for each of nodes distributed along the boundary of the plate of interest. In addition, a new way of decreasing the size of the system matrix that gives natural frequencies of the plate is employed to reduce the amount of numerical calculations, which is needed for computing the determinant of the system matrix. Finally the excellence of the characteristics of convergence and accuracy of the method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate and converged swiftly to exact values as the number of boundary nodes increases.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.1
• /
• pp.105-116
• /
• 2003

The flow structure around the free end of a finite circular cylinder (FC) embedded in an atmospheric boundary layer (ABL) over open terrain was investigated experimentally with varying the free end shape. The experiments were carried out in a closed-return type subsonic wind tunnel. A finite cylinder with an aspect ratio (L/D) of 6 was mounted vertically on a long flat plate. The Reynolds number based on the cylinder diameter is about Re=7,500. The velocity fields near the FC free end were measured using the single-frame double-exposure PIV method. As a result, for the FC with a right-angled free end, there is a peculiar vortical structure, showing counter-rotating twin vortices near the FC free end. It is caused by the interaction between the entrained irrotational fluids from both sides of FC and the downwash flow from the FC free-end.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
• /
• 2001.04a
• /
• pp.77-80
• /
• 2001

The element-free Galerkin (EFG) method is one of meshless methods, which is an efficient method of modeling problems of fluid or solid mechanics with complex boundary shapes and large changes in boundary conditions. This paper discusses the theory of the EFG method and its applications to modeling of groundwater flow. In the EFG method, shape functions are constructed based on the moving least square (MLS) approximation, which requires only set of nodes. The EFG method can eliminate time-consuming mesh generation procedure with irregular shaped boundaries because it does not require any elements. The coupled EFG-FEM technique was introduced to treat Dirichlet boundary conditions. A computer code EFGG was developed and tested for the problems of steady-state and transient groundwater flow in homogeneous or heterogeneous aquifers. The accuracy of solutions by the EFG method was similar to that by the FEM. The EFG method has the advantages in convenient node generation and flexible boundary condition implementation.

• Journal of KSNVE
• /
• v.4 no.2
• /
• pp.137-146
• /
• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.

• Journal of the Society of Naval Architects of Korea
• /
• v.41 no.4
• /
• pp.38-44
• /
• 2004

The motion response analysis of a submerged elliptic cylinder in waves is presented and the elliptic cylinder is a simplification of the section of submarine in this paper. The method is based on boundary integral method and two-dimensional 3 degree motions are calculated in regular harmonic waves. The fully nonlinear free surface boundary condition is assumed in an numerical domain and this solution is matched along an assumed boundary as a linear solution composed of transient Green function, The large amplitude motions of an elliptic cylinder are directly simulated and effects of wave frequency, wave amplitude and the distance from buoyancy center to gravity center are discussed.

• Journal of Ocean Engineering and Technology
• /
• v.26 no.5
• /
• pp.55-62
• /
• 2012

In this paper, the rigid lid boundary condition is applied to simulate the influence of floating structures such as ships or pontoons, and the pressure term in both the momentum equations and continuity equation are modified. The pressure of a floating structure under the free surface is dependent on the draft of the structure, generally called a ship. If the free surface is covered by a floating structure, the free surface cannot move freely. The water level should be fixed, using a rigid lid boundary condition. This boundary condition is implemented by reducing the storage area of the grid cell with a factor between zero and one. The numerical model developed by Hong (2009) is verified through a comparison with experimental results, and the influence of the reduction factor is investigated using the verified numerical model.

• Structural Engineering and Mechanics
• /
• v.72 no.1
• /
• pp.1-17
• /
• 2019

This paper proposes a modified matched interface and boundary (MMIB) method to analyze the free vibration of beams with various interfaces caused by steps, intermediate rigid and elastic supports, intermediate concentrated masses and spring-mass systems, etc. A new strategy is developed to determine the parameters in the iterative computation of MMIB. The MMIB procedures are established to deal with boundary conditions and various interface conditions, which overcomes the shortcoming of the traditional MIB. A number of examples are utilized to illustrate the performance of MMIB method. Numerical results indicate that the MMIB method is a highly accurate and convergent approach for solving interface problems.

• Journal of the Society of Naval Architects of Korea
• /
• v.34 no.4
• /
• pp.53-60
• /
• 1997

Nonlinear free surface flow phenomena have teen studied by several kinds of numerical methods, of which boundary element method has been known as most promising one. There, however, remain many difficulties to be solved in the numerical procedures by boundary element analysis. In this paper, an efficient calculation of elemental integrals and iterative solution algorithm for the resulting system of equations were thoroughly investigated in order to enhance the procedure of the boundary element analysis. Advantages of the herein developed boundary element analysis code are demonstrated in terms of accuracy and convergence for typical boundary-value problems with free surface.

• Journal of the Society of Naval Architects of Korea
• /
• v.29 no.3
• /
• pp.80-89
• /
• 1992

This paper deals with the open boundary problems, and two numerical schemes are used for the implementation of open boundary condition. One is to add the artificial damping term to dynamic free-surface boundary condition. Determination of suitable damping coefficient and the damping cone is the most important in this scheme. The other scheme is a modified Orlanski's method. This will be useful for the problems with unidirectional waves. A few typical free-surface wave problems are modeled for the numerical test. Method of solution is fundamental source-distribution method and the fully nonlinear boundary conditions are applied. The computed results are compared with those of others for the proof of practicality of these schemes.