• Journal of applied mathematics & informatics
• /
• v.36 no.1_2
• /
• pp.135-154
• /
• 2018

In this paper, an almost second order overlapping Schwarz method for singularly perturbed third order convection-diffusion type problem is constructed. 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 combination of classical finite difference scheme and central finite difference scheme on a uniform mesh while on the non-layer region we use the midpoint difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. We proved that, when appropriate subdomains are used, the method produces convergence of second order. 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 are it reduce iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Journal of applied mathematics & informatics
• /
• v.38 no.1_2
• /
• pp.113-132
• /
• 2020

In this paper, a class of linear second order singularly perturbed delay differential turning point problems containing a small delay (or negative shift) on the reaction term and when the solution of the problem exhibits twin boundary layers are examined. A hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the problem. We proved that the method is almost second order ε-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.31-48
• /
• 2010

In this article, we consider singularly perturbed Boundary Value Problems(BVPs) for second order Ordinary Differential Equations (ODEs) with Neumann boundary condition and discontinuous source term. A parameter-uniform error bound for the solution is established using the Streamline-Diffusion Finite Element Method (SDFEM) on a piecewise uniform meshes. We prove that the method is almost second order of convergence in the maximum norm, independently of the perturbation parameter. Further we derive superconvergence results for scaled derivatives of solution of the same problem. Numerical results are provided to substantiate the theoretical results.

• Journal of the Korean Institute of Telematics and Electronics S
• /
• v.34S no.1
• /
• pp.65-71
• /
• 1997

In this paper, we propose a new .mu.-controller design method using an equivalent weighting function $W_{\mu}$(s). The proposed mehtod is not guaranteed to converge to the minimum as D-K and .mu.-K iteration method. However, the robust performance problem can be converted into an equivalent $H^{\infty}$ optimization problem of unstructured uncertainty by using an equivalent weightng function $W_{\mu}$(s). Also we can find a .mu.-optimal controller iteratively using an error index $d_{\epsilon}$ of differnce between maximum singular value and .mu.-norm. And under the condition of the same order of scaling functions, the proposed method provides the .mu.-optimal controller with the degree less than that obtained by D-K iteration..

• Proceedings of the IEEK Conference
• /
• 2002.07b
• /
• pp.1220-1223
• /
• 2002

In this paper, numerical robust stability analysis method and its design are presented. L$_2$robust stability of the fuzzy system is analyzed by casting the systems into the diagonal norm bounded linear differential inclusions (DNLDI) formulation. Based on the linear matix inequality (LMI) optimization programming, a numerical method for finding the maximum stable ranges of the fuzzy feedback linarization control gains is proposed.

• 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.

• Journal of Institute of Control, Robotics and Systems
• /
• v.2 no.3
• /
• pp.158-164
• /
• 1996

In this paper, we consider the problem of robust stability of discretd time-delay systems subjected to perturbations. Two classes of perturbations are treated. The first one is the nonlinear norm-bounded perturbation, and the second is the structured time-varying parametric perturbation. Based on the discrete-time Lyapunov stability theory, several new sufficient conditions for robust stability of the system are presented. From these conditions, we can estimate the maximum allowable bounds of the perturbations which guarantee the stability. Finally, numerical examples are given to demonstrate the effectiveness of the results.

• 제어로봇시스템학회:학술대회논문집
• /
• 1987.10b
• /
• pp.193-197
• /
• 1987

Decentralized model reference adaptive controller is used to control interconnected system. Influences caused by interactions between each subsystem are regarded as unmodeled dynamics or disturbances, thus decentralized adaptive controller is designed using MRAC algorithms which guarantees robustness. To expand the stability regions of over all system and to improve control performances, higher level controller is introduced to adjust the control factors such as filter band, size of deadzone or maximum norm of parameter. Local controllers for each subsystem are realized in real time and higher level controller has an ability of detecting the instability phenomena and adjusts the local controller by analysis of power spectrum or square sum of tracking errors.

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 2009.01a
• /
• pp.103-107
• /
• 2009

This paper presents how to minimize the second-order cone programming problem occurring in the 3D reconstruction of multiple views. The $L_{\infty}$-norm minimization is done by a series of the minimization of the maximum infeasibility. Since the problem has many inequality constraints, we have to adopt methods of the interior point algorithm, in which the inequalities are sequentially approximated by log-barrier functions. An initial feasible solution is found easily by the construction of the problem. Actual computing is done by an iterative Newton-style update. When we apply the interior point method to the problem of reconstructing the structure and motion, every Newton update requires to solve a very large system of linear equations. We show that the sparse bundle-adjustment technique can be utilized in the same way during the Newton update, and therefore we obtain a very efficient computation.

• The korean journal of orthodontics
• /
• v.21 no.3
• /
• pp.481-493
• /
• 1991

The purpose of this study was to obtain the norm of the crown shape (tip, torque, in/out) and arch form, and to provide basic data for fabricating straight wire bracket and ideal arch wire for Korean. 100 subjects aged from 17 to 26 (50 females, 50 males) were selected with a normal occlusion. By measuring the size, angulation, inclination, arch width, facial prominance of the teeth and the molar offset, the following results were obtained. 1. Average, standard deviation, minimum, maximum of each measuring item for each teeth were obtained. 2. Intermolar width (${\underline{6}}$ to ${\underline{6}}$) of upper arch before occlusal surface cutting and intermolar width of upper arch (${\underline{6}}$ to ${\underline{6}}$, ${\underline{7}}$ to ${\underline{7}}$) after occlusal surface cutting showed statistical difference. There was no difference between sexes in any other measuring items. 3. Arch form and specification of straight wire bracket for Korean who have normal occlusion was obtained.