• Journal of applied mathematics & informatics
• /
• v.8 no.3
• /
• pp.683-691
• /
• 2001

A linearized finite-difference scheme is used to transform the initial/boundary-value problem associated with the nonlinear Schrodinger equation into a linear algebraic system. This method is developed by replacing the time and the nonlinear term by an appropriate parametric linearized scheme based on Taylor’s expansion. The resulting finite-difference method is analysed for stability and convergence. The results of a number of numerical experiments for the single-soliton wave are given.

• Journal of applied mathematics & informatics
• /
• v.36 no.3_4
• /
• pp.181-203
• /
• 2018

In this paper, we have constructed an overlapping Schwarz method for singularly perturbed second order convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the central finite difference scheme on a uniform mesh while on the non-layer region we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. When appropriate subdomains are used, the numerical approximations generated from the method are shown to be first order convergent. Furthermore it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme is it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.24 no.9
• /
• pp.1227-1238
• /
• 2000

This study examines the effects of the discretization schemes on numerical solutions of viscoelastic fluid flows. For this purpose, a temporally evolving mixing layer, a two-dimensional vortex pair interacting with a wall, and a turbulent channel flow are selected as the test cases. We adopt a fourth-order compact scheme (COM4) for polymeric stress derivatives in the momentum equations. For convective derivatives in the constitutive equations, the first-order upwind difference scheme (UD) and artificial diffusion scheme (AD), which are commonly used in the literature, show most stable and smooth solutions even for highly extensional flows. However, the stress fields are smeared too much and the flow fields are quite different from those obtained by higher-order upwind difference schemes for the same flow parameters. Among higher-order upwind difference schemes, a third-order compact upwind difference scheme (CUD3) shows most stable and accurate solutions. Therefore, a combination of CUD3 for the convective derivatives in the constitutive equations and COM4 for the polymeric stress derivatives in the momentum equations is recommended to be used for numerical simulation of highly extensional flows.

• Journal of applied mathematics & informatics
• /
• v.8 no.1
• /
• pp.45-57
• /
• 2001

A parametric scheme is proposed for the numerical solution of the nonlinear Boussinesq equation. The numerical method is developed by approximating the time and the space partical derivatives by finite-difference re placements and the nonlinear term by an appropriate linearized scheme. The resulting finite-difference method is analyzed for local truncation error and stability. The results of a number of numerical experiments are given for both the single and the double-soliton wave. AMS Mathematics Subject Classification : 65J15, 47H17, 49D15.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.53-68
• /
• 2004

Numerical solutions for the viscous Cahn-Hilliard equation are considered using the Crank-Nicolson type finite difference method which conserves the mass. The corresponding stability and error analysis of the scheme are shown. The decay speeds of the solution in $H^1-norm$ are shown. We also compare the evolution of the viscous Cahn-Hilliard equation with that of the Cahn-Hilliard equation numerically and computationally, which has been given as an open question in Novick-Cohen[13].

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.22 no.3
• /
• pp.201-215
• /
• 2018

In this paper we consider a class of singularly perturbed system of delay differential equations of convection diffusion type with integral boundary conditions. A finite difference scheme on an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete maximum norm. Numerical experiments support our theoretical results.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.16 no.4
• /
• pp.27-32
• /
• 2006

Broadcast Encryption allows a center to broadcast encrypted message to a set of users so that only privileged users can decrypt them. In this paper, we propose an efficient broadcast encryption scheme based on the 'Subset Difference' (SD) scheme. It reduces the transmission overhead by 50 percent while the storage overhead remains the same but the computational overhead somewhat increases.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.7 no.2
• /
• pp.75-81
• /
• 2003

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.

• Journal of The Institute of Information and Telecommunication Facilities Engineering
• /
• v.5 no.1
• /
• pp.37-42
• /
• 2006

A reversible audio watermarking algorithm is presented in this paper. This algorithm transforms the audio signal with the integer wavelet transform first in order to enhance the correlation between neighbor audio samples. Audio signal has low correlation between neighbor samples, which makes it difficult to apply difference expansion scheme. Second, a novel difference expansion scheme is used to embed more data by reducing the size of location map. Therefore, the difference expansion scheme used in this paper theoretically secures high embedding capacity under low perceptual distortion. Experiments show that this scheme can hide large number of information bits and keeps high perceptual quality.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.2
• /
• pp.467-474
• /
• 1993

Viscous flow and heat transfer phenomena in an axisymmetric cylinder which models a diesel engine have been numerically studied. In order to search for a way to minimize numerical diffusion, the effectiveness and the appropriateness of two selected numerical schemes for convective terms in the governing equations have been tested. They are Linear Upwind Difference Scheme and Hybrid Scheme. Using a standard k-.epsilon. turbulence model, the calculation has been carried out basically up to 180.deg. of crank angle. As a result, it was shown from comparison with previous experimental data that Linear Upwind Difference Scheme is less influenced than Hybrid Scheme by the numerical diffusion and it was suggested that these effects of numerical diffusion can be more significant than those due to turbulence modeling.